Answer:
Explanation:
Let's call the amount of money Mary had initially "X" (in dollars).
According to the information given:
If she bought 4 blouses, she would be short of $6. This means that the cost of 4 blouses is $6 more than her initial amount.
So, the cost of 4 blouses is X - 6 dollars.
If she used the same amount of money to buy 3 blouses and 2 belts, she would be left with $3. The total cost of 3 blouses and 2 belts is equal to her initial amount plus $3.
So, 3 times the cost of 1 blouse plus 2 times the cost of 1 belt is equal to X + $3.
Now, we are also given that each belt costs $5. Therefore, the cost of 2 belts is 2 * $5 = $10.
Now we can set up a system of equations based on the information:
4 * Cost of 1 blouse = X - 6
3 * Cost of 1 blouse + 2 * $5 = X + $3
Let's solve this system of equations:
From the first equation, we can express the cost of 1 blouse:
Cost of 1 blouse = (X - 6) / 4
Now, substitute this expression into the second equation:
3 * ((X - 6) / 4) + $10 = X + $3
Now, let's solve for X:
3 * (X - 6) / 4 + $10 = X + $3
Multiply both sides by 4 to get rid of the fraction:
3 * (X - 6) + 40 = 4 * (X + 3)
Now, distribute the 3 on the left side:
3X - 18 + 40 = 4X + 12
Combine like terms:
3X + 22 = 4X + 12
Subtract 3X from both sides:
22 = X + 12
Subtract 12 from both sides:
X = 22 - 12
X = 10
So, Mary initially had $10. Therefore:
The cost of 1 blouse is (X - 6) / 4 = ($10 - $6) / 4 = $4 / 4 = $1.
The cost of 2 belts is 2 * $5 = $10.
Mary had enough money to buy 3 blouses and 2 belts, and she had $3 left, which matches our calculations:
3 * $1 + 2 * $5 = $3 + $10 = $13
So, the given information is consistent, and Mary had $10 to start with.