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# The difference between two numbers is 16. Five times the smaller is the same as 8 less than twice the larger. find the numbers.

You most use a system of two equations in two variables. I need help please.

### 2 Answers by Expert Tutors

Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
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Hi Alexander;
x...smaller number
x+16...larger number
5x=[2(x+16)]-8
Distribute the 2...
5x=2x+32-8
Combine like terms...
5x=2x+24
Subtract 2x from both sides...
5x-2x=2x-2x+24
3x=24
Divide both sides by 3...
(3x)/3=24/3
x=8
x+16=24
Let's check our work...
(5)(8)=[(2)(24)]-8
40=48-8
40=40

Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
5.0 5.0 (9 lesson ratings) (9)
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let x be the larger number
let y be the smaller number

x-y=16
5y=2x-8
x-y=16, x=y+16
substitute y+16 for x in the equation 5y=2x-8
5y=2(y+16)-8
5y=2y+32-8
5y=2y+24
5y-2y=2y-2y+24
3y=24
y=8
x-8=16
x=24
the larger number is 24 and the smaller number is 8
check:5*8=40 and 2*24=48
40 is 8 less than 48