SOLUTION: the sum of two number is 35. twice the first number is equal to 5 times the second number. find the two numbers

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Question 1149226: the sum of two number is 35. twice the first number is equal to 5 times the second number. find the two numbers
Answer by greenestamps(13200) (Show Source):
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There are multiple options for how to solve this problem. For a beginning algebra class, something like this might be appropriate.

Let x = first number
let y = second number

The sum of the two numbers is 35: x+y=35 (1)
Twice the first is equal to 5 times the second: 2x = 5y (2)

Solve either equation for one variable in terms of the other and substitute in the other equation. One option would be

y = 35-x

and then

2x = 5(35-x)

Solve that equation for x and then substitute that value in one of the original equations to find y.

My personal preference for solving this problem would be this....

"twice the first number is equal to 5 times the second number"
--> the two numbers are in the ratio 5:2
--> let the two numbers be 5x and 2x

Then

5x+2x = 35
7x = 35
x = 5

The two numbers are 5x=25 and 2x=10.

Hopefully you will get responses from other tutors showing different methods....