Peter and Cindy each had some money at first. Peter started spending $1.20 daily.
After 15 days, Cindy started spending 1 2/3 of what Peter spent daily. When CIndy
spent all of her money, she had spent $11.60 more than Peter.
a) How many days did Cindy take to spend all of her money?
b) How much did Peter spend in total when Cindy spent all of her money?
If they started with $p and $c, respectively, then after d days, they had left
p - 1.20d
c - 5/3 * 1.20 (d-15)
c=0 after d = 15 + c/2 days
at that point, Peter had spent 6/5 (15 + c/2)
c = 6/5 (15 + c/2) + 11.60
c = 74
check:
Cindy spent $2/day so she spent $74 in 37 days
Peter had spent 74.00-11.60 at 1.20 per day, in 52 = 37+15 days
To solve the problem, we'll break it down into steps:
Let's start by finding out Peter's total spending after 15 days.
Peter's spending per day = $1.20
Number of days = 15
Peter's total spending = Peter's spending per day * Number of days
= $1.20 * 15
= $18
So, Peter spent a total of $18 after 15 days.
Now, let's find out how much Cindy spent per day.
Cindy's daily spending = 1 2/3 of what Peter spent daily
To find out the value of 1 2/3, we can convert it to a mixed number:
1 2/3 = 3/3 + 2/3 = 5/3
Cindy's daily spending = $1.20 * (5/3)
= $2.00
Now, let's find out how much Cindy spent more than Peter.
Cindy's extra spending per day = Cindy's daily spending - Peter's daily spending
= $2.00 - $1.20
= $0.80
We are given that Cindy spent $11.60 more than Peter. So, we can calculate the number of days it took for Cindy to spend all of her money.
Number of days Cindy took = Extra spending / Cindy's extra spending per day
= $11.60 / $0.80
= 14.5
Since we cannot have a fraction of a day, we round the answer to the closest whole number. Therefore, Cindy took about 15 days to spend all of her money.
Finally, let's calculate how much Peter spent in total when Cindy spent all of her money.
Peter's total spending when Cindy spent all of her money = Peter's total spending after 15 days + Cindy's extra spending
= $18 + $11.60
= $29.60
So, Peter spent a total of $29.60 when Cindy spent all of her money.
a) Cindy took about 15 days to spend all of her money.
b) Peter spent a total of $29.60 when Cindy spent all of her money.