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

Click here to post comments

Join in and write your own page! It's easy to do. How? Simply click here to return to System of linear equations.

Recent Articles

  1. How to Write an Inequality

    Dec 12, 19 07:51 AM

    Learn how to write an inequality quickly with this easy to follow math lesson.

    Read More

New math lessons

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

                                 Follow me on Pinterest

Real Life Math Skills

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