Claudio a banking vice president took 17 neckties to Milto Cleaners. The rate for non silk ties is $3.25 per tie and for silk ties is $3.60 per tie. His total bill was $58.75. How many silk ties did he have dry cleaned?
Can you please show work on how to solve this?
S*3.6+ (17-S)3.25=58.75
Is that correct?
A classmate said the answer is 10 silk neckties. I need help working through the whole problem.
I will be happy to check and critique your work. I am not going to do it for you.
To solve this problem, we can set up a system of equations. Let's denote the number of non-silk ties as 'x' and the number of silk ties as 'y.'
According to the problem, Claudio took a total of 17 ties to the cleaners, so we have the equation:
x + y = 17 ----(1)
The problem also tells us that the cost of cleaning non-silk ties is $3.25 per tie and the cost of cleaning silk ties is $3.60 per tie. The total bill was $58.75, so we can set up the second equation:
3.25x + 3.60y = 58.75 ----(2)
We now have a system of two equations with two variables. We can solve this system by using substitution or elimination. Let's use the elimination method:
Multiply equation (1) by 3.25 to make the coefficients of 'x' in both equations the same:
3.25(x + y) = 3.25(17)
3.25x + 3.25y = 55.25 ----(3)
Now, we can subtract equation (3) from equation (2) to eliminate 'x':
3.25x + 3.60y - (3.25x + 3.25y) = 58.75 - 55.25
0.35y = 3.50
Divide both sides of the equation by 0.35:
y = 3.50 / 0.35
y = 10
Therefore, Claudio had 10 silk ties dry cleaned.