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Two numbers differ by 5. Seven times the smaller plus four times the larger is 108. Find the number

User Peter Liaw
by
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1 Answer

2 votes

Answer:

8 and 13

Explanation:

Given

Let both numbers be a and b where a > b

So:


a- b =5 --- Their difference


7b + 4a = 108 --- 7 of smaller and 4 of bigger

Required

Find both numbers


a- b =5 --- (1)


7b + 4a = 102 --- (2)

Make a the subject in (1)


a = b + 5

Substitute b + 5 for (a) in (2)


7b + 4(b + 5) = 108

Open bracket


7b + 4b + 20 = 108

Collect like terms


7b + 4b = 108 - 20


11b = 88

Divide both sides by 11


b = (88)/(11)


b = 8

Substitute 8 for b in
a = b + 5


a = 8 + 5


a = 13

Hence the two numbers are 8 and 13

User Matthew Read
by
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