SOLUTION: Karlie and Tara go on a One Direction spending spree. Karlie buys 2 used microphones and 6 of Niall's shoelaces spending a total of $808. Tara buys 3 used microphones and 14 of N

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Question 887304: Karlie and Tara go on a One Direction spending spree. Karlie buys 2 used microphones and 6 of Niall's shoelaces spending a total of $808. Tara buys 3 used microphones and 14 of Niall's shoelaces spending a total of #1302. How much was a used microphone? How much was one of Niall's shoelaces?
Answer by algebrapro18(249) (Show Source):
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Lets start off by letting M be the price of a used microphone and lets let S be the price of the shoelaces. We know that Karlie buys 2 used microphones and 6 of Niall's shoelaces and that she spent $808. An equation to express this mathematically would be:

2M+6S = 808

We also know that tara bought 3 used microphones and 14 of Niall's shoelaces and spent $1,302. An equation to express this would be:

3M+14S=$1,302.

So now we have two equations and two unknowns(the price of the used microphone and shoe laces). If we look at the first equation we notice that everything in it is divisible by 2 which is the number of microphones that Karlie bought. So lets solve the first equation for M or the price of the used microphones.

2M + 6S = 808 subtract 6s from both sides
2M = 808 - 6S divide both sides by 2
M = 404 - 3S

Now that we have an equation for the price for the used microphone we can substitute that in for M in the second equation and solve for S.

3M + 14S = $1,302 Substitue M=404-3S into the equation
3(404 - 3S) + 14s = 1302 Distribute
1212 - 9S + 14S = 1302 Combine like terms
1212 + 5S = 1302 Subtract 1212 from both sides
5S = 90 divide by 5
S = 18.

So we know that one of Niall's shoe laces is selling for 18 bucks. We can now plug that back into the equation for the price of the microphone to find out how much a used microphone is going for.

M = 404 - 3S Substitute the 18 bucks in for S
M = 404 - 3(18) Combine like terms
M = $350

So we know that a used microphone is $350 and a pair of shoelaces were $18.