# SOLVE IT

by Visticious Loverial
(Austria)

The sum of four numbers a, b, c, and d is 68. If we increase a by 7, we get x. If we increased b by 8, we get x. If we decrease c by 15, we get 2x.If we multiply d by 4, we get x. What is the value of x?

Solution

The problem gives the following 5 equations

a + b + a + d = 68 (1)

a + 7 = x (2)

b + 8 = x (3)

c - 15 = 2x (4)

d x 4 = x (5)

Use equations (2),(3), (4),and (5) to solve for a, b, c, and d.

a + 7 = x

a + 7 - 7 = x - 7

a = x - 7

b + 8 = x

b + 8 - 8 = x - 8

b = x - 8

c - 15 = 2x

c - 15 + 15 = 2x + 15

c = 2x + 15

d x 4 = x

(d x 4)/4 = x / 4

d = x / 4

Replace a, b, c, and d into equation (1)

x - 7 + x - 8 + 2x + 15 + x / 4 = 68

x + x + 2x - 7 - 8 + 15 + x / 4 = 68

4x - 15 + 15 + x / 4 = 68

4x + x / 4 = 68

Multiply everything by 4

4 times 4x + 4 times (x / 4) + 4 times 68

16x + x = 272

17x = 272

Since 17 x 16 = 272, x = 16

## Recent Articles

1. ### Overtime Calculator - How much for Time and a Half or Double rate ?

Jan 18, 19 10:53 AM

This overtime calculator will help you figure out how much money earned for working overtime

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

## Recent Lessons

1. ### Overtime Calculator - How much for Time and a Half or Double rate ?

Jan 18, 19 10:53 AM

This overtime calculator will help you figure out how much money earned for working overtime

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests.

Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.