William is 3 years, older than Charmine. The sum of 3 times Charmaine's age and 2 times William's age is 76. How old are William

Question

NikAS [45]

3 years ago

7

William is 3 years, older than Charmine. The sum of 3 times Charmaine's age and 2 times William's age is 76. How old are William

and Charmaine? Show your work

Mathematics

1 answer:

lana66690 [7] · Answer 1 · 2022-05-27T16:15:38+03:00

William is 17 years old and Charmaine is 14 years old.

Step-by-step explanation:

Let x be the age of William and y be the age of Charmaine

Then

William is 3 years, older than Charmine.

x = y+3 Eqn 1

The sum of 3 times Charmaine's age and 2 times William's age is 76.

2x+3y = 76 Eqn 2

Putting x = y+3 in Eqn 2

$2(y+3)+3y=76\\2y+6+3y=76\\5y+6=76\\Subtracting\ 6\ from\ both\ sides\\5y+6-6=76-6\\5y=70\\Dividing\ both\ sides\ by\ 5\\\frac{5y}{5} = \frac{70}{5}\\y=14\\Putting\ the\ value\ of\ y\ in\ Eqn\ 1\\x=y+3\\x=14+3\\x=17$

Hence,

William is 17 years old and Charmaine is 14 years old.

Keywords: Linear equations, Variables

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