a company sells brass and steel machine parts. One shipment contain 3 brass and 10 steel parts and cost 48.00. A second shipment contain 7 brass and 4 steel parts and cost 54.00. Find the cost of each type of machine part. How much would a shipment containing 10 brass and 13 steel machine parts cost?
Cost of brass part = x
Cost of steel part = y
2x + 10y = 48
7x + 4y = 54
solve for x and y
( I would multiply the first by 2, and the second by 5, then subtract them)
To find the cost of each type of machine part, we can represent the cost of brass parts as "x" and the cost of steel parts as "y".
From the information given in the first shipment, we know that 3 brass parts and 10 steel parts cost $48. This can be written as:
3x + 10y = 48 ...equation 1
Similarly, from the information given in the second shipment, we know that 7 brass parts and 4 steel parts cost $54. This can be written as:
7x + 4y = 54 ...equation 2
We now have a system of two equations with two variables. We can solve this system to find the values of "x" and "y".
To do this, we can use either substitution or elimination method. Let's use the elimination method to solve the system of equations:
Step 1: Multiply equation 1 by 7 and equation 2 by 3 to get the same coefficient for "x":
21x + 70y = 336 ...equation 3
21x + 12y = 162 ...equation 4
Step 2: Subtract equation 4 from equation 3 to eliminate "x" variable:
21x - 21x + 70y - 12y = 336 - 162
58y = 174
y = 174 / 58
y = 3
Step 3: Substitute the value of y = 3 into equation 1:
3x + 10(3) = 48
3x + 30 = 48
3x = 48 - 30
3x = 18
x = 18 / 3
x = 6
Therefore, the cost of each brass machine part is $6 and the cost of each steel machine part is $3.
To find the cost of a shipment containing 10 brass and 13 steel machine parts, we can multiply the number of each type of part with their respective costs:
Cost of 10 brass parts = 10 x $6 = $60
Cost of 13 steel parts = 13 x $3 = $39
Therefore, a shipment containing 10 brass and 13 steel machine parts would cost $60 + $39 = $99.