A hardware store makes a mixed bag of 42 items using screws, bolts, and washers. The cost of screws are $3.00 each, bolts cost $
2.00 each, and washers are $1.50 each. The mixture calls for four times as many screws than bolts. The total cost of the mixture is $102.00. How much of each item did the store use.
s - the number of screws b - the number of bolts w - the number of washes
<span>The cost of screws are $3.00 each: 3s </span><span>The cost of bolts are $2.00 each: 2b </span><span>The cost of washers are $1.0 each: 1.5w
</span><span>A hardware store makes a mixed bag of 42 items using screws, bolts, and washers: s + b + w = 42 </span><span>The mixture calls for four times as many screws than bolts: s = 4b </span>The total cost of the mixture is $102.00: 3s + 2b + 1.5w = 102
The system of three equations: (i) s + b + w = 42 (ii) s = 4b (iii) 3s + 2b + 1.5w = 102
Substitute s from (ii) equation into (i) equation and express it in the term of w: 4b + b + w = 42 5b + w = 42 w = 42 - 5b
Substitute s from (ii) equation and w from (i) equation into (iii) equation: 3 * 4b + 2b + 1.5(42 - 5b) = 102 12b + 2b + 63 - 7.5b = 102 6.5b + 63 = 102 6.5b = 102 - 63 6.5b = 39 b = 39 : 6.5 b = 6
