Aloysius and Benjamin have $150 altogether. Aloysius' mother gives him another $40 and Benjamin spends $ 10 on a book. Benjamin then has $10 more than Aloysius . How much money does each of them have at first?

Aloy has $55 initially

Benjamin has $95 initially

Step-by-step explanation:

In this question, given the order in which the money flowed in the question, we want to know how much each of the two had initially.

let what Aloys have be x and what Benjamin has be y.

Together, they had 150

x + y = 150 ••••••••(i)

Aloys mother gave him 40, new money is x + 40, Benjamin spent 10, new money is y-10

the new difference is 10

Thus;

(x + 40)-(y-10) = 10

x + 40 -y + 10 = 10

x+ 40 = y

substitute this into the first equation

x + 40 + x = 150

2x + 40 = 150

2x = 150-40

2x = 110

x = 110/2

x = $55

y = x + 40 = 55 + 40 = $95