Kyle spends an equal amount of money each day. After 4 days, he had 4/5 of his money left. After another 10 days he had $30 left. How much money did Kyle begin with?

4 days spending equal amounts so if x is how much he spends per day and y is the original amount then 4x=1/5y bc he has 4/5 left meaning what he spent was 1/5 of the original and after 10 more days which was 14 total he spent all but 30 so the total minus 30 will be how much kyle spent so

14x=y-30 which is y = (14x+30) and substitute that in for y in 4x=1/5y so 4x=1/5 (14x+30)

20x=14x+30

6x=30

x=5 and plug that in either of the original equations 4 (5) = 1/5y

y=100

so he had $100 and spent $5 per day

In 4 days he spends 1/5 of his money

to find unit amount per day

1/5 divided by 4

which equals 1/20

kyle spends 1/20 of his total money per day

so after 14 days, he has spent 14/20 of his money

20/20-14/20=6/20 or the amount of money he has left

6/20=$30

if 6/20=$30, then 1/20 equals $5 (30/6)

if 1/20 of Kyles money = $5

5*20 = $100

kyle started with $100