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.