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.

Answer 1

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 ✔

Answer 2

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