Answer:
The value of x is 3.
Step-by-step explanation:
Matthew earned 7500 of 15000, which is exactly half the total amount, meaning that the fraction corresponding to his earnings is 1/2.
Rate of 5:2:x, with number 5 corresponding to Matthew, mean that his fraction of the earnings, in function of x is given by:
[tex]\frac{5}{5 + 2 + x} = \frac{5}{7 + x}[/tex]
Both fractions are equal, so:
[tex]\frac{5}{7 + x} = \frac{1}{2}[/tex]
Applying cross multiplication:
[tex]7 + x = 10[/tex]
[tex]x = 10 - 7[/tex]
[tex]x = 3[/tex]
The value of x is 3.
