Sarah was given a sum of money. She spent the same amount of money each day. She spent 2/7 of her money in 6 days. After another 5 days, she had $20 left. How much money did she have at first.
let the amount she spent each day be $x
so in the 6 days she spent 6x
This was 2/7 of her total
(2/7)total = 6x
total = (7/2)(6x) = 21x
so 21x - 5x = 20
16x = 20
x = 20/16 = 1.25
So she spent $1.25 each day
her total at the start was 21x = $26.25
check:
after 5 days, she spent 5(1.25) = 6.25
leaving her with $20 , ✔
in 6 days she spent 6(1.25) = $7.50
leaving her with 26.25-7.5 = $18.75
... and what is 2/7 of $26.25 ???
it is $7.5 ✔
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To find out how much money Sarah had at first, we can start by finding out how much money she spent each day.
Let's assume Sarah started with x dollars. She spent the same amount of money each day, so she spent a total of (2/7)x dollars in 6 days.
We know that after another 5 days, she had $20 left. So, in total, she spent (6 + 5) = 11 days.
Now, let's find out how much money Sarah spent each day. We can express this as:
(2/7)x / 6 dollars per day
To find out how much money Sarah spent in 11 days, we can multiply the money spent per day by the number of days:
(2/7)x / 6 * 11
We know the amount spent in 11 days is equal to the starting amount minus $20:
(2/7)x / 6 * 11 = x - 20
Now, we can solve this equation to find the value of x, which represents the initial amount of money Sarah had.