Solved on Jan 09, 2024

Green pepper plants grew 5 inches in $\frac{3}{4}$ months. Find the growth in feet per month.

STEP 1

Assumptions
1. The green pepper plants grew 5 inches in $\frac{3}{4}$ months.
2. There are 12 inches in one foot.
3. The growth rate is constant over time.

STEP 2

First, we need to find the growth rate of the green pepper plants per month. We can do this by dividing the growth in inches by the number of months.
$Growth\, rate\, per\, month = \frac{Growth\, in\, inches}{Number\, of\, months}$

STEP 3

Now, plug in the given values for the growth in inches and the number of months to calculate the growth rate per month.
$Growth\, rate\, per\, month = \frac{5\, inches}{\frac{3}{4}\, months}$

STEP 4

To simplify the division by a fraction, we multiply by the reciprocal of the fraction.
$Growth\, rate\, per\, month = 5\, inches \times \frac{4}{3}$

STEP 5

Calculate the growth rate per month.
$Growth\, rate\, per\, month = 5\, inches \times \frac{4}{3} = \frac{20}{3}\, inches\, per\, month$

STEP 6

Now, we want to convert the growth rate from inches per month to feet per month. Since there are 12 inches in one foot, we divide the number of inches by 12.
$Growth\, rate\, in\, feet\, per\, month = \frac{Growth\, rate\, in\, inches\, per\, month}{12}$

STEP 7

Plug in the value for the growth rate in inches per month to calculate the growth rate in feet per month.
$Growth\, rate\, in\, feet\, per\, month = \frac{\frac{20}{3}\, inches}{12}$

STEP 8

Simplify the fraction by dividing 20 by 12.
$Growth\, rate\, in\, feet\, per\, month = \frac{20}{3} \times \frac{1}{12}\, feet$

STEP 9

Calculate the growth rate in feet per month.
$Growth\, rate\, in\, feet\, per\, month = \frac{20}{3} \times \frac{1}{12} = \frac{20}{36}\, feet\, per\, month$

STEP 10

Simplify the fraction $\frac{20}{36}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 4.
$Growth\, rate\, in\, feet\, per\, month = \frac{20 \div 4}{36 \div 4} = \frac{5}{9}\, feet\, per\, month$
The green pepper plants can grow $\frac{5}{9}$ feet per month.

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Green pepper plants grew 5 inches in $\frac{3}{4}$ months. Find the growth in feet per month.

STEP 1

Assumptions
1. The green pepper plants grew 5 inches in $\frac{3}{4}$ months.
2. There are 12 inches in one foot.
3. The growth rate is constant over time.

STEP 2

First, we need to find the growth rate of the green pepper plants per month. We can do this by dividing the growth in inches by the number of months.
$Growth\, rate\, per\, month = \frac{Growth\, in\, inches}{Number\, of\, months}$

STEP 3

Now, plug in the given values for the growth in inches and the number of months to calculate the growth rate per month.
$Growth\, rate\, per\, month = \frac{5\, inches}{\frac{3}{4}\, months}$

STEP 4

To simplify the division by a fraction, we multiply by the reciprocal of the fraction.
$Growth\, rate\, per\, month = 5\, inches \times \frac{4}{3}$

STEP 5

Calculate the growth rate per month.
$Growth\, rate\, per\, month = 5\, inches \times \frac{4}{3} = \frac{20}{3}\, inches\, per\, month$

STEP 6

Now, we want to convert the growth rate from inches per month to feet per month. Since there are 12 inches in one foot, we divide the number of inches by 12.
$Growth\, rate\, in\, feet\, per\, month = \frac{Growth\, rate\, in\, inches\, per\, month}{12}$

STEP 7

Plug in the value for the growth rate in inches per month to calculate the growth rate in feet per month.
$Growth\, rate\, in\, feet\, per\, month = \frac{\frac{20}{3}\, inches}{12}$

STEP 8

Simplify the fraction by dividing 20 by 12.
$Growth\, rate\, in\, feet\, per\, month = \frac{20}{3} \times \frac{1}{12}\, feet$

STEP 9

Calculate the growth rate in feet per month.
$Growth\, rate\, in\, feet\, per\, month = \frac{20}{3} \times \frac{1}{12} = \frac{20}{36}\, feet\, per\, month$

STEP 10

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Green pepper plants grew 5 inches in 34\frac{3}{4}43​ months. Find the growth in feet per month.

STEP 1

Assumptions1. The green pepper plants grew 5 inches in 34\frac{3}{4}43​ months.2. There are 12 inches in one foot.3. The growth rate is constant over time.

STEP 2

STEP 3

Now, plug in the given values for the growth in inches and the number of months to calculate the growth rate per month.Growth rate per month=5 inches34 monthsGrowth\, rate\, per\, month = \frac{5\, inches}{\frac{3}{4}\, months}Growthratepermonth=43​months5inches​

STEP 4

To simplify the division by a fraction, we multiply by the reciprocal of the fraction.Growth rate per month=5 inches×43Growth\, rate\, per\, month = 5\, inches \times \frac{4}{3}Growthratepermonth=5inches×34​

STEP 5

Calculate the growth rate per month.Growth rate per month=5 inches×43=203 inches per monthGrowth\, rate\, per\, month = 5\, inches \times \frac{4}{3} = \frac{20}{3}\, inches\, per\, monthGrowthratepermonth=5inches×34​=320​inchespermonth

STEP 6

STEP 7

Plug in the value for the growth rate in inches per month to calculate the growth rate in feet per month.Growth rate in feet per month=203 inches12Growth\, rate\, in\, feet\, per\, month = \frac{\frac{20}{3}\, inches}{12}Growthrateinfeetpermonth=12320​inches​

STEP 8

Simplify the fraction by dividing 20 by 12.Growth rate in feet per month=203×112 feetGrowth\, rate\, in\, feet\, per\, month = \frac{20}{3} \times \frac{1}{12}\, feetGrowthrateinfeetpermonth=320​×121​feet

STEP 9

Calculate the growth rate in feet per month.Growth rate in feet per month=203×112=2036 feet per monthGrowth\, rate\, in\, feet\, per\, month = \frac{20}{3} \times \frac{1}{12} = \frac{20}{36}\, feet\, per\, monthGrowthrateinfeetpermonth=320​×121​=3620​feetpermonth

STEP 10

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Green pepper plants grew 5 inches in $\frac{3}{4}$ months. Find the growth in feet per month.

Assumptions
1. The green pepper plants grew 5 inches in $\frac{3}{4}$ months.
2. There are 12 inches in one foot.
3. The growth rate is constant over time.

Now, plug in the given values for the growth in inches and the number of months to calculate the growth rate per month.
$Growth\, rate\, per\, month = \frac{5\, inches}{\frac{3}{4}\, months}$

To simplify the division by a fraction, we multiply by the reciprocal of the fraction.
$Growth\, rate\, per\, month = 5\, inches \times \frac{4}{3}$

Calculate the growth rate per month.
$Growth\, rate\, per\, month = 5\, inches \times \frac{4}{3} = \frac{20}{3}\, inches\, per\, month$

Plug in the value for the growth rate in inches per month to calculate the growth rate in feet per month.
$Growth\, rate\, in\, feet\, per\, month = \frac{\frac{20}{3}\, inches}{12}$

Simplify the fraction by dividing 20 by 12.
$Growth\, rate\, in\, feet\, per\, month = \frac{20}{3} \times \frac{1}{12}\, feet$

Calculate the growth rate in feet per month.
$Growth\, rate\, in\, feet\, per\, month = \frac{20}{3} \times \frac{1}{12} = \frac{20}{36}\, feet\, per\, month$