Answer to Question #88587 in Algebra for Marcus

Question

An MTN cellular-phone user notices that her cellular phone accounts for three
consecutive months were significantly different. In May, her account was one and a half
times more than her account in June. Her account in July was R 50 more than her account in
June. In total, she spent R575 in cellular-phone accounts in the three months. What was her
account for each month?

Answer 1

$x_1$ - R was spent in May

$x_2$ - R was spent in June

$x_3$ - R was spent in July

Construct the system of equations:

$$x_1 = 1.5 * x_2$$ $$x_2 = x_3 - 50$$ $$x_1 + x_2 + x_3 = 575$$

Since $x_2 = x_3 - 50$ and $x_1 = 1,5 * x_2$ thus:

$1.5 * (x_3 - 50) + x_3 - 50 + x_3 = 575$

$1.5 * x_3 + x_3 + x_3 = 575 + 50 + 75$

$3.5 * x_3 = 700$

$x_3 = 200$

Find x₂ :

$x_2 = x_3 - 50 = 200 - 50 = 150$

Find x₁ :

$x_1 = 1.5 * x_2 = 1.5 * 150 = 225$

Answer:

May: x₁ = 225

June: x₂ = 150

July: x₃ = 200