Mrs hart spent 3/5 of her money on a bag. 1/6 on a belt . She has 14 dollars left. How much money did she have in the beginning ?
x - 3/5 x - 1/6 x = 14
7/30 x = 14
x = 60
check:
36 on bag
10 on belt
leaves 14
To find out how much money Mrs. Hart had in the beginning, let's break down the problem step by step.
Let's start with the information given:
Mrs. Hart spent 3/5 of her money on a bag.
Mrs. Hart spent 1/6 of her money on a belt.
She has $14 left.
To find out the total amount of money Mrs. Hart had at the beginning, we need to work backwards.
Step 1: Calculate the remaining fraction of money Mrs. Hart has left.
Since she has $14 left and this represents the remaining fraction of her money, we need to subtract this fraction from 1 (since 1 represents the whole amount of money).
1 - 14/Total Amount of Money = Fraction of Money Spent
Step 2: Calculate the fraction of money Mrs. Hart spent on the bag.
Mrs. Hart spent 3/5 of her money on the bag, so the fraction of money spent on the bag is 3/5.
Step 3: Calculate the fraction of money Mrs. Hart spent on the belt.
Mrs. Hart spent 1/6 of her money on the belt, so the fraction of money spent on the belt is 1/6.
Step 4: Set up an equation using the fractions of money spent.
The remaining money fraction (from Step 1) should equal the sum of the fractions spent on the bag and the belt.
Fraction of Money Spent on Bag + Fraction of Money Spent on Belt = Fraction of Money Remaining
3/5 + 1/6 = remaining money fraction
Step 5: Solve the equation to find the remaining money fraction.
To solve this equation, we need a common denominator for 5 and 6, which is 30.
(18/30) + (5/30) = remaining money fraction
23/30 = remaining money fraction
Step 6: Calculate the total amount of money.
We now know that the remaining money fraction, 23/30, represents $14.
23/30 = $14
To find the total amount of money, we set up a ratio:
23/30 = $14/x
Cross-multiplying, we get:
23x = 30 * $14
23x = $420
Finally, divide both sides by 23 to solve for x:
x = $420 / 23
Approximately, x = $18.26
So, Mrs. Hart had approximately $18.26 in the beginning.