Samantha went shopping and spent half her money on a T-shirt and a third of her money on a scarf. She returned with $15. How much money did she have to begin with?
My working out:
s = money to begin with
s - 1/2
s - 1/3 = 15
1/2 S=T
1/3 S=scarf
so, S-1/2S-1/3 s=15
S(1-1/2-1/3)=15
S(6-3-2)/6=15
S(1)=90
goodness, she blew that 90 dollars away. 45 dollars on a T? 30 dollars on a Scarf?
Just checking, the space between the s (money to begin with) and the fractions is multiplication? Thanks so much for your help.
To solve this problem, we can set up an equation based on the information given in the problem.
Let's use "s" to represent the amount of money Samantha had to begin with.
According to the problem, Samantha spent half of her money on a T-shirt, which can be represented as (1/2)s. Similarly, she spent a third of her money on a scarf, which can be represented as (1/3)s.
After deducting these expenses, we know that Samantha had $15 remaining. So, we can write the equation:
s - (1/2)s - (1/3)s = 15
To solve this equation, we need to find a common denominator for the fractions. In this case, the least common multiple (LCM) of 2 and 3 is 6. So, we multiply the whole equation by 6 to eliminate the fractions:
6s - 3s - 2s = 90
Combining like terms, we have:
s - 90 = 90
Now, isolate the variable:
s = 90 + 15
s = 105
Therefore, Samantha had $105 to begin with.