Question

One number is times a first number. A third number is 100 more than the first number. If the sum of the three numbers is ​, find the numbers. The three numbers are nothing. ​(Use a comma to separate answers as​ needed.)

Answer 1

Question:

One number is 7 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 505, Find the numbers.

Answer:

The numbers are 45, 315 and 145

Explanation:

Represent the three numbers with A, B and C

Required

Find A, B and C

From the first statement;

`B = 7 * A`

`B = 7A` --- (i)

From the second;

`C = 100 + A` ---- (ii)

From the third;

`A + B + C = 505` ---- (iii)

Substitute 7A for B and 100 + A for C in (iii)

`A + 7A + 100 + A = 505`

Collect like terms

`A + 7A + A = 505 - 100`

`9A = 405`

Divide both sides by 9

`A = 45`

Substitute 45 for A in (i)

`B = 7A`

`B = 7 * 45`

`B = 315`

Substitute 45 for A in (ii)

`C = 100 + A`

`C = 100 + 45`

`C = 145`

Hence, the numbers are 45, 315 and 145