SOLUTION: Emma buys some cans at 28 pences each, and twice as many cans of orange at 22 pences each. She also buys ten fewer cans of lemonade than orange at 25 pences each. She spends 14.58

Question 204236This question is from textbook Longman Mathematics for IGCSE Book 1
: Emma buys some cans at 28 pences each, and twice as many cans of orange at 22 pences each. She also buys ten fewer cans of lemonade than orange at 25 pences each. She spends 14.58 pounds. How many cans of cola did she buy?
This question is from textbook Longman Mathematics for IGCSE Book 1

Found 2 solutions by Theo, rfer:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Emma buys some cans of cola at 28 pence each, and twice as many cans of orange at 22 pence each. She also buys ten fewer cans of lemonade than orange at 25 pence each. She spends 14.58 pounds. How many cans of cola did she buy?
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let x = number of cans of cola
let y = number of cans of orange
let z = number of cans of lemonade
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total cost:
28x + 22y + 25z = 14.58 pounds
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number of pence to the pound is 100 (after decimalization in 1971)
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total costs equation becomes:
28x + 22y + 25z = 1458 pence
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number of cans of orange is twice number of cans of cola
y = 2x
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number of cans of lemonade is 10 less than number of cans of orange
z = y-10
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total number of cans = x + y + z
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we have:
x = number of cans of cola
y = number of cans of orange = 2x
z = number of cans of lemonade = y-10 = 2x-10
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we can solve for x in the equation on total cost.
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equation of 28x + 22y + 25z = 1458 pence becomes:
28x + 22*(2x) + 25*(2x-10) = 1458
that equation becomes:
28x + 44x + 50x - 250 = 1458
add 250 to both sides of the equation and combine like terms to get:
122x = 1708
divide both sides by 122 to get:
x = 14
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x = 14
y = 2x = 28
z = y-10 = 18
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the money equation was:
28x + 22y + 25z = 1458 pence
substituting the number of cans for x, y, and z, that equation becomes:
28*14 + 22*28 + 25*18 = 1458 pence
that equation becomes:
392 + 616 + 450 = 1458
which becomes:
1458 = 1458
which is true so the values for x,y,z are good.
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answer to the question:
she bought 14 cans of cola.
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Answer by rfer(16322) (Show Source): You can put this solution on YOUR website!

c=28x=14 cans
o=22(2x)=28 cans
25(2x-10)= 18 cans
28x+22(2x)+25(2x-10)=1458
122x-250=1458
122x=1708
x=14
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