Question

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?

Answer 1

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

Answer 2

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