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Solved on Jan 22, 2024

Matthew bought 3 kg3 \mathrm{~kg} of walnuts at $7.34/kg\$ 7.34/\mathrm{kg} and 5 kg5 \mathrm{~kg} of almonds at $6.87/kg\$ 6.87/\mathrm{kg}. He paid with a $100\$ 100 bill. What is his change?

STEP 1

Assumptions
1. Matthew bought 3 kg3 \mathrm{~kg} of walnuts.
2. The cost of walnuts per kilogram is $7.34\$ 7.34.
3. Matthew bought 5 kg5 \mathrm{~kg} of almonds.
4. The cost of almonds per kilogram is $6.87\$ 6.87.
5. Matthew gave the cashier a $100\$ 100 bill.
6. We need to calculate the total cost and then subtract it from $100\$ 100 to find the change.

STEP 2

First, we need to calculate the total cost of the walnuts. We can do this by multiplying the quantity of walnuts by the cost per kilogram.
Total cost of walnuts=Quantity of walnuts×Cost per kilogram of walnutsTotal\, cost\, of\, walnuts = Quantity\, of\, walnuts \times Cost\, per\, kilogram\, of\, walnuts

STEP 3

Now, plug in the given values for the quantity of walnuts and the cost per kilogram to calculate the total cost of walnuts.
Total cost of walnuts=3 kg×$7.34 per kgTotal\, cost\, of\, walnuts = 3 \mathrm{~kg} \times \$ 7.34\, per\, \mathrm{kg}

STEP 4

Calculate the total cost of walnuts.
Total cost of walnuts=3×$7.34=$22.02Total\, cost\, of\, walnuts = 3 \times \$ 7.34 = \$ 22.02

STEP 5

Next, we need to calculate the total cost of the almonds. We can do this by multiplying the quantity of almonds by the cost per kilogram.
Total cost of almonds=Quantity of almonds×Cost per kilogram of almondsTotal\, cost\, of\, almonds = Quantity\, of\, almonds \times Cost\, per\, kilogram\, of\, almonds

STEP 6

Now, plug in the given values for the quantity of almonds and the cost per kilogram to calculate the total cost of almonds.
Total cost of almonds=5 kg×$6.87 per kgTotal\, cost\, of\, almonds = 5 \mathrm{~kg} \times \$ 6.87\, per\, \mathrm{kg}

STEP 7

Calculate the total cost of almonds.
Total cost of almonds=5×$6.87=$34.35Total\, cost\, of\, almonds = 5 \times \$ 6.87 = \$ 34.35

STEP 8

Now that we have the total cost of walnuts and almonds, we can find the total cost of all the nuts combined.
Total cost of nuts=Total cost of walnuts+Total cost of almondsTotal\, cost\, of\, nuts = Total\, cost\, of\, walnuts + Total\, cost\, of\, almonds

STEP 9

Plug in the values for the total cost of walnuts and almonds to calculate the total cost of nuts.
Total cost of nuts=$22.02+$34.35Total\, cost\, of\, nuts = \$ 22.02 + \$ 34.35

STEP 10

Calculate the total cost of nuts.
Total cost of nuts=$22.02+$34.35=$56.37Total\, cost\, of\, nuts = \$ 22.02 + \$ 34.35 = \$ 56.37

STEP 11

To find out how much change Matthew should get back, we subtract the total cost of nuts from the amount he gave the cashier ($100\$ 100).
Change=Amount given−Total cost of nutsChange = Amount\, given - Total\, cost\, of\, nuts

STEP 12

Plug in the values for the amount given and the total cost of nuts to calculate the change.
Change=$100−$56.37Change = \$ 100 - \$ 56.37

STEP 13

Calculate the change Matthew should get back.
Change=$100−$56.37=$43.63Change = \$ 100 - \$ 56.37 = \$ 43.63
Matthew should get back $43.63\$ 43.63 in change.

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