A camping store put in an order for flashlights and sleeping bags. The number of flashlights ordered was 3 times the number of sleeping bags. The flashlights cost $12.00 each, and the sleeping bags cost $45.00 each. If the total cost for the flashlights and the sleeping bags was $1215.00, how many flashlights and how many sleeping bags did they order?
Let F = number of Flashlights
Let S = number of Sleeping Bags
F = 3S since the number of flashlights is three times the number of sleeping bags.
The value of the flashlighs is 12F
The value of the sleeping bags is 45S
The two equations are:
F = 3S
12F + 45S = 1215
Substitute the 3S for the F in the second equation.
12(3S) + 45 S = 1215.
solve for S, then find F in the original first equation.
Let's break down the problem step by step:
Let's assume the number of sleeping bags ordered is "x".
According to the given information, the number of flashlights ordered is 3 times the number of sleeping bags, which means the number of flashlights ordered is 3x.
Now, we can calculate the cost of sleeping bags. Since the sleeping bags cost $45 each and the number of sleeping bags is "x", the total cost of sleeping bags is 45x.
Similarly, we can calculate the cost of flashlights. Since the flashlights cost $12 each and the number of flashlights is 3x, the total cost of flashlights is 12 * (3x) or 36x.
According to the problem, the total cost of both sleeping bags and flashlights is $1215. So we can write the equation:
45x + 36x = 1215
Combining the like terms, we get:
81x = 1215
To solve for x, we divide both sides of the equation by 81:
x = 1215 / 81
x = 15
Now that we know x (the number of sleeping bags), we can calculate the number of flashlights:
Number of flashlights = 3x = 3 * 15 = 45
Therefore, the camping store ordered 45 flashlights and 15 sleeping bags.