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5 votes
Can anyone help?

Mary buys 5 pears and 2 kiwi fruits for £3.90 and Dave
buys 3 pears and 1 kiwi fruit for £2.20 Find the cost of a
pear and the cost of a kiwi fruit.
Pear = £
Kiwi = £

1 Answer

3 votes

Answers:

Pear = £0.50

Kiwi = £0.70

You may or may not need to type in the pound sign.

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Work Shown

x = cost of 1 pear

y = cost of 1 kiwi

5x+2y = 3.90 is from the first sentence in the instructions

3x+1y = 2.20 is from the second sentence

Double both sides of the 2nd equation to get 6x+2y = 4.40

We get this equivalent system

5x+2y = 3.90

6x+2y = 4.4

Subtract straight down.

  • The x terms subtract to 5x-6x = -1x = -x
  • The y terms cancel out
  • The right hand side terms subtract to 3.90 - 4.40 = -0.5

Therefore, we get -x = -0.5 which leads to x = 0.50

Each pear costs £0.50 or 50 pence.

Use that x value in either of the equations mentioned to find y.

3x+y = 2.20

3*0.5 + y = 2.20

1.50 + y = 2.20

y = 2.20 - 1.50

y = 0.70

Each kiwi costs £0.70 or 70 pence.

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Check

Mary buys 5 pears and 2 kiwi at unit prices £0.50 and £0.70 respectively

Her total cost is 5*0.50 + 2*0.70 = 3.90 pounds

The answer is confirmed with Mary.

Let's now check Dave.

He buys 3 pears and 1 kiwi at those same unit prices, so he spends a total of 3*0.50 + 1*0.70 = 2.20 pounds.

The answer is confirmed with Dave as well.

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Another way to check:

Use a tool like Desmos or GeoGebra to plot these equations

5x+2y = 3.90

3x+1y = 2.20

They intersect at the point (0.50, 0.70) as shown in the diagram below.

This then leads to x = 0.50 and y = 0.70

These values are exact and haven't been rounded.

Helpful tip: With Desmos you click on the point of intersection to have the coordinates show up. You may have to click twice.

Can anyone help? Mary buys 5 pears and 2 kiwi fruits for £3.90 and Dave buys 3 pears-example-1
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