Sandra has some money she spends 2/7 of it on a book & she spends 2/5 of the remaining money on a bag Sandra has $15 left how much did she have to start
amount of her money --- x
after spending 2/7 of it, she has (5/7)x left
then she spends (2/5) of that, or (2/5)(5/7)x
total amount spent = (2/7)x + (10/35)x
= (2/7)x + (2/7)x = (4/7)x
so (3/7)x = 15
3x = 105
x = 35 <------ money she started with
check:
she spends (2/7)(35) or 10
leaving her with 25
she spends (2/5) of that or 10
leaving her with 15
my answer is correct
To find out how much Sandra had to start, we can follow a step-by-step approach.
Let's assume that the amount Sandra had to start with is "x" dollars.
Step 1: She spends 2/7 of her money on a book.
After buying the book, the remaining money with Sandra will be (1 - 2/7) of x.
Simplifying this expression, we get (5/7) * x.
Step 2: She spends 2/5 of the remaining money on a bag.
After buying the bag, the remaining money will be (1 - 2/5) of (5/7) * x.
Simplifying this expression, we get (3/5) * (5/7) * x.
Step 3: She has $15 left.
According to the question, Sandra has $15 left, so we can set up the equation:
(3/5) * (5/7) * x = $15.
To solve this equation, we can follow these steps:
1. Simplify the fraction (3/5)*(5/7) to get (3/7).
So, the equation becomes: (3/7)*x = $15.
2. Multiply both sides of the equation by 7/3 to isolate x.
By doing this, the equation becomes: x = ($15)*(7/3).
3. Simplify the right side of the equation.
$15 multiplied by (7/3) gives us $35.
Therefore, Sandra had $35 to start with.