# Solve a simple system with five equations

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

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