Solved on Feb 09, 2024

Find the total amounts of nitrogen ( $N$ ), phosphoric acid ( $P_2O_5$ ), and potash ( $K_2O$ ) in a mixture of 200 pounds of Vigoro and 500 pounds of Parker's fertilizers.

STEP 1

Assumptions
1. Vigoro Ultra Turf fertilizer contains 29% nitrogen, 3% phosphoric acid, and 4% potash by weight.
2. Parker's Premium Starter fertilizer contains 18% nitrogen, 25% phosphoric acid, and 6% potash by weight.
3. We have 200 pounds of Vigoro and 500 pounds of Parker's.
4. We need to find the total amount of each nutrient in the mixture.

STEP 2

First, calculate the amount of each nutrient in the 200 pounds of Vigoro fertilizer.
$Nitrogen_{Vigoro} = 200 \text{ pounds} \times \frac{29}{100}$

STEP 3

Calculate the amount of nitrogen in the 200 pounds of Vigoro fertilizer.
$Nitrogen_{Vigoro} = 200 \times 0.29$

STEP 4

Calculate the actual amount of nitrogen in Vigoro.
$Nitrogen_{Vigoro} = 58 \text{ pounds}$

STEP 5

Calculate the amount of phosphoric acid in the 200 pounds of Vigoro fertilizer.
$Phosphoric\, acid_{Vigoro} = 200 \text{ pounds} \times \frac{3}{100}$

STEP 6

Calculate the actual amount of phosphoric acid in Vigoro.
$Phosphoric\, acid_{Vigoro} = 200 \times 0.03$

STEP 7

Calculate the actual amount of phosphoric acid in Vigoro.
$Phosphoric\, acid_{Vigoro} = 6 \text{ pounds}$

STEP 8

Calculate the amount of potash in the 200 pounds of Vigoro fertilizer.
$Potash_{Vigoro} = 200 \text{ pounds} \times \frac{4}{100}$

STEP 9

Calculate the actual amount of potash in Vigoro.
$Potash_{Vigoro} = 200 \times 0.04$

STEP 10

Calculate the actual amount of potash in Vigoro.
$Potash_{Vigoro} = 8 \text{ pounds}$

STEP 11

Now, calculate the amount of each nutrient in the 500 pounds of Parker's fertilizer.
$Nitrogen_{Parker's} = 500 \text{ pounds} \times \frac{18}{100}$

STEP 12

Calculate the amount of nitrogen in the 500 pounds of Parker's fertilizer.
$Nitrogen_{Parker's} = 500 \times 0.18$

STEP 13

Calculate the actual amount of nitrogen in Parker's.
$Nitrogen_{Parker's} = 90 \text{ pounds}$

STEP 14

Calculate the amount of phosphoric acid in the 500 pounds of Parker's fertilizer.
$Phosphoric\, acid_{Parker's} = 500 \text{ pounds} \times \frac{25}{100}$

STEP 15

Calculate the actual amount of phosphoric acid in Parker's.
$Phosphoric\, acid_{Parker's} = 500 \times 0.25$

STEP 16

Calculate the actual amount of phosphoric acid in Parker's.
$Phosphoric\, acid_{Parker's} = 125 \text{ pounds}$

STEP 17

Calculate the amount of potash in the 500 pounds of Parker's fertilizer.
$Potash_{Parker's} = 500 \text{ pounds} \times \frac{6}{100}$

STEP 18

Calculate the actual amount of potash in Parker's.
$Potash_{Parker's} = 500 \times 0.06$

STEP 19

Calculate the actual amount of potash in Parker's.
$Potash_{Parker's} = 30 \text{ pounds}$

STEP 20

Now, add the amounts of each nutrient from both types of fertilizers to get the total amount in the mixture.
$Total\, nitrogen = Nitrogen_{Vigoro} + Nitrogen_{Parker's}$

STEP 21

Calculate the total amount of nitrogen in the mixture.
$Total\, nitrogen = 58 + 90$

STEP 22

Calculate the total nitrogen.
$Total\, nitrogen = 148 \text{ pounds}$

STEP 23

Calculate the total amount of phosphoric acid in the mixture.
$Total\, phosphoric\, acid = Phosphoric\, acid_{Vigoro} + Phosphoric\, acid_{Parker's}$

STEP 24

Calculate the total phosphoric acid.
$Total\, phosphoric\, acid = 6 + 125$

STEP 25

Calculate the total phosphoric acid.
$Total\, phosphoric\, acid = 131 \text{ pounds}$

STEP 26

Calculate the total amount of potash in the mixture.
$Total\, potash = Potash_{Vigoro} + Potash_{Parker's}$

STEP 27

Calculate the total potash.
$Total\, potash = 8 + 30$

STEP 28

Calculate the total potash.
$Total\, potash = 38 \text{ pounds}$
The mixture contains 148 pounds of nitrogen, 131 pounds of phosphoric acid, and 38 pounds of potash.

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Find the total amounts of nitrogen (NNN), phosphoric acid (P2O5P_2O_5P2​O5​), and potash (K2OK_2OK2​O) in a mixture of 200 pounds of Vigoro and 500 pounds of Parker's fertilizers.

STEP 1

STEP 2

First, calculate the amount of each nutrient in the 200 pounds of Vigoro fertilizer.NitrogenVigoro=200 pounds×29100Nitrogen_{Vigoro} = 200 \text{ pounds} \times \frac{29}{100}NitrogenVigoro​=200 pounds×10029​

STEP 3

Calculate the amount of nitrogen in the 200 pounds of Vigoro fertilizer.NitrogenVigoro=200×0.29Nitrogen_{Vigoro} = 200 \times 0.29NitrogenVigoro​=200×0.29

STEP 4

Calculate the actual amount of nitrogen in Vigoro.NitrogenVigoro=58 poundsNitrogen_{Vigoro} = 58 \text{ pounds}NitrogenVigoro​=58 pounds

STEP 5

Calculate the amount of phosphoric acid in the 200 pounds of Vigoro fertilizer.Phosphoric acidVigoro=200 pounds×3100Phosphoric\, acid_{Vigoro} = 200 \text{ pounds} \times \frac{3}{100}PhosphoricacidVigoro​=200 pounds×1003​

STEP 6

Calculate the actual amount of phosphoric acid in Vigoro.Phosphoric acidVigoro=200×0.03Phosphoric\, acid_{Vigoro} = 200 \times 0.03PhosphoricacidVigoro​=200×0.03

STEP 7

Calculate the actual amount of phosphoric acid in Vigoro.Phosphoric acidVigoro=6 poundsPhosphoric\, acid_{Vigoro} = 6 \text{ pounds}PhosphoricacidVigoro​=6 pounds

STEP 8

Calculate the amount of potash in the 200 pounds of Vigoro fertilizer.PotashVigoro=200 pounds×4100Potash_{Vigoro} = 200 \text{ pounds} \times \frac{4}{100}PotashVigoro​=200 pounds×1004​

STEP 9

Calculate the actual amount of potash in Vigoro.PotashVigoro=200×0.04Potash_{Vigoro} = 200 \times 0.04PotashVigoro​=200×0.04

STEP 10

Calculate the actual amount of potash in Vigoro.PotashVigoro=8 poundsPotash_{Vigoro} = 8 \text{ pounds}PotashVigoro​=8 pounds

STEP 11

Now, calculate the amount of each nutrient in the 500 pounds of Parker's fertilizer.NitrogenParker′s=500 pounds×18100Nitrogen_{Parker's} = 500 \text{ pounds} \times \frac{18}{100}NitrogenParker′s​=500 pounds×10018​

STEP 12

Calculate the amount of nitrogen in the 500 pounds of Parker's fertilizer.NitrogenParker′s=500×0.18Nitrogen_{Parker's} = 500 \times 0.18NitrogenParker′s​=500×0.18

STEP 13

Calculate the actual amount of nitrogen in Parker's.NitrogenParker′s=90 poundsNitrogen_{Parker's} = 90 \text{ pounds}NitrogenParker′s​=90 pounds

STEP 14

Calculate the amount of phosphoric acid in the 500 pounds of Parker's fertilizer.Phosphoric acidParker′s=500 pounds×25100Phosphoric\, acid_{Parker's} = 500 \text{ pounds} \times \frac{25}{100}PhosphoricacidParker′s​=500 pounds×10025​

STEP 15

Calculate the actual amount of phosphoric acid in Parker's.Phosphoric acidParker′s=500×0.25Phosphoric\, acid_{Parker's} = 500 \times 0.25PhosphoricacidParker′s​=500×0.25

STEP 16

Calculate the actual amount of phosphoric acid in Parker's.Phosphoric acidParker′s=125 poundsPhosphoric\, acid_{Parker's} = 125 \text{ pounds}PhosphoricacidParker′s​=125 pounds

STEP 17

Calculate the amount of potash in the 500 pounds of Parker's fertilizer.PotashParker′s=500 pounds×6100Potash_{Parker's} = 500 \text{ pounds} \times \frac{6}{100}PotashParker′s​=500 pounds×1006​

STEP 18

Calculate the actual amount of potash in Parker's.PotashParker′s=500×0.06Potash_{Parker's} = 500 \times 0.06PotashParker′s​=500×0.06

STEP 19

Calculate the actual amount of potash in Parker's.PotashParker′s=30 poundsPotash_{Parker's} = 30 \text{ pounds}PotashParker′s​=30 pounds

STEP 20

Now, add the amounts of each nutrient from both types of fertilizers to get the total amount in the mixture.Total nitrogen=NitrogenVigoro+NitrogenParker′sTotal\, nitrogen = Nitrogen_{Vigoro} + Nitrogen_{Parker's}Totalnitrogen=NitrogenVigoro​+NitrogenParker′s​

STEP 21

Calculate the total amount of nitrogen in the mixture.Total nitrogen=58+90Total\, nitrogen = 58 + 90Totalnitrogen=58+90

STEP 22

Calculate the total nitrogen.Total nitrogen=148 poundsTotal\, nitrogen = 148 \text{ pounds}Totalnitrogen=148 pounds

STEP 23

Calculate the total amount of phosphoric acid in the mixture.Total phosphoric acid=Phosphoric acidVigoro+Phosphoric acidParker′sTotal\, phosphoric\, acid = Phosphoric\, acid_{Vigoro} + Phosphoric\, acid_{Parker's}Totalphosphoricacid=PhosphoricacidVigoro​+PhosphoricacidParker′s​

STEP 24

Calculate the total phosphoric acid.Total phosphoric acid=6+125Total\, phosphoric\, acid = 6 + 125Totalphosphoricacid=6+125

STEP 25

Calculate the total phosphoric acid.Total phosphoric acid=131 poundsTotal\, phosphoric\, acid = 131 \text{ pounds}Totalphosphoricacid=131 pounds

STEP 26

Calculate the total amount of potash in the mixture.Total potash=PotashVigoro+PotashParker′sTotal\, potash = Potash_{Vigoro} + Potash_{Parker's}Totalpotash=PotashVigoro​+PotashParker′s​

STEP 27

Calculate the total potash.Total potash=8+30Total\, potash = 8 + 30Totalpotash=8+30

STEP 28

Calculate the total potash.Total potash=38 poundsTotal\, potash = 38 \text{ pounds}Totalpotash=38 poundsThe mixture contains 148 pounds of nitrogen, 131 pounds of phosphoric acid, and 38 pounds of potash.

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Find the total amounts of nitrogen ( $N$ ), phosphoric acid ( $P_2O_5$ ), and potash ( $K_2O$ ) in a mixture of 200 pounds of Vigoro and 500 pounds of Parker's fertilizers.

First, calculate the amount of each nutrient in the 200 pounds of Vigoro fertilizer.
$Nitrogen_{Vigoro} = 200 \text{ pounds} \times \frac{29}{100}$

Calculate the amount of nitrogen in the 200 pounds of Vigoro fertilizer.
$Nitrogen_{Vigoro} = 200 \times 0.29$

Calculate the actual amount of nitrogen in Vigoro.
$Nitrogen_{Vigoro} = 58 \text{ pounds}$

Calculate the amount of phosphoric acid in the 200 pounds of Vigoro fertilizer.
$Phosphoric\, acid_{Vigoro} = 200 \text{ pounds} \times \frac{3}{100}$

Calculate the actual amount of phosphoric acid in Vigoro.
$Phosphoric\, acid_{Vigoro} = 200 \times 0.03$

Calculate the actual amount of phosphoric acid in Vigoro.
$Phosphoric\, acid_{Vigoro} = 6 \text{ pounds}$

Calculate the amount of potash in the 200 pounds of Vigoro fertilizer.
$Potash_{Vigoro} = 200 \text{ pounds} \times \frac{4}{100}$

Calculate the actual amount of potash in Vigoro.
$Potash_{Vigoro} = 200 \times 0.04$

Calculate the actual amount of potash in Vigoro.
$Potash_{Vigoro} = 8 \text{ pounds}$

Now, calculate the amount of each nutrient in the 500 pounds of Parker's fertilizer.
$Nitrogen_{Parker's} = 500 \text{ pounds} \times \frac{18}{100}$

Calculate the amount of nitrogen in the 500 pounds of Parker's fertilizer.
$Nitrogen_{Parker's} = 500 \times 0.18$

Calculate the actual amount of nitrogen in Parker's.
$Nitrogen_{Parker's} = 90 \text{ pounds}$

Calculate the amount of phosphoric acid in the 500 pounds of Parker's fertilizer.
$Phosphoric\, acid_{Parker's} = 500 \text{ pounds} \times \frac{25}{100}$

Calculate the actual amount of phosphoric acid in Parker's.
$Phosphoric\, acid_{Parker's} = 500 \times 0.25$

Calculate the actual amount of phosphoric acid in Parker's.
$Phosphoric\, acid_{Parker's} = 125 \text{ pounds}$

Calculate the amount of potash in the 500 pounds of Parker's fertilizer.
$Potash_{Parker's} = 500 \text{ pounds} \times \frac{6}{100}$

Calculate the actual amount of potash in Parker's.
$Potash_{Parker's} = 500 \times 0.06$

Calculate the actual amount of potash in Parker's.
$Potash_{Parker's} = 30 \text{ pounds}$

Now, add the amounts of each nutrient from both types of fertilizers to get the total amount in the mixture.
$Total\, nitrogen = Nitrogen_{Vigoro} + Nitrogen_{Parker's}$

Calculate the total amount of nitrogen in the mixture.
$Total\, nitrogen = 58 + 90$

Calculate the total nitrogen.
$Total\, nitrogen = 148 \text{ pounds}$

Calculate the total amount of phosphoric acid in the mixture.
$Total\, phosphoric\, acid = Phosphoric\, acid_{Vigoro} + Phosphoric\, acid_{Parker's}$

Calculate the total phosphoric acid.
$Total\, phosphoric\, acid = 6 + 125$

Calculate the total phosphoric acid.
$Total\, phosphoric\, acid = 131 \text{ pounds}$

Calculate the total amount of potash in the mixture.
$Total\, potash = Potash_{Vigoro} + Potash_{Parker's}$

Calculate the total potash.
$Total\, potash = 8 + 30$

Calculate the total potash.
$Total\, potash = 38 \text{ pounds}$
The mixture contains 148 pounds of nitrogen, 131 pounds of phosphoric acid, and 38 pounds of potash.