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. Quadratic Formula: Easy To Follow Steps

    Jan 26, 23 11:44 AM

    Quadratic formula
    Learn about the quadratic formula, the discriminant, important definitions related to the formula, and applications.

    Read More

  2. Area Formula - List of Important Formulas

    Jan 25, 23 05:54 AM

    Frequently used area formulas
    What is the area formula for a two-dimensional figure? Here is a list of the ones that you must know!

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

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

Math quizzes

 Recommended

Math vocabulary quizzes