Question

World problem Algebra 2. A mom buys 3 different types if t-shirts for her children, long sleeve, polo, and short sleeve. The long sleeve shirts cost $18 each, the polos cost $15 each, and the short sleeve cost $12 each. The mother purchased 3 less polos then she did short sleeve shirts. If the mother purchased 18 shirts at an average of $14 each, find the number of each type of shirt purchased

Answer 1

@satellite73 could you help me me set of the equations?

Answer 2

start by declaring your variable
say "let \(x\) = ..."

Answer 3

i set up p= s-3 and 18L + 15p+ 12s = 18 but Ihave a feelings there not right

Answer 4

no it is not right
\[18L+15P+12S\] represents the cost, not the total number of shirts bought

Answer 5

if \(L\) is the number of long sleeve shirts, then the cost of all the long sleeve shirts is \(18L\) etc
the total number of all the shirts is
\[P+L+S\], which you know to be 18 so you can write
\[P+L+S=18\] as one equation

Answer 6

now we have to figure out how much was spent all together. she bought 18 shirts at an average of $14 per shirt so that shouldn't be too hard

Answer 7

let me know when you get the answer (by multiplying)

Answer 8

252

Answer 9

ok good, so now we have 3.6*5
\[P+L+S=18\]\[18L+15P+12S=252\]and also \[P=S-3\]

Answer 10

ignore that weird number up top, it is a type

Answer 11

now lets go back and replace all the \(P\) what we see by \(S-3\)

Answer 12

\[S-3+L+S=18\]\[15(S-3)+18L+12S=252\]

Answer 13

we still have a bit more work to do because this problem is annoying
first equation become
\[2S+L-3=18\] or
\[2S+L=21\]

Answer 14

is that our final equation?

Answer 15

oh no we also have the second equation which (after multiplying out and collecting terms) will be
\[18L+27S=297\]

Answer 16

whew this is a pain right? we have to solve the two equation
\[2S+L=21\]\[18L+27S=297\] so we can do this by rewriting the first equation as
\[L=21-2S\]substitute in the second one to get
\[18(21-2S)+27S=297\] and FINALLY we have one equation to solve

Answer 17

hopefully after a bit of algebra you will get \(S=9\)

Answer 18

and of course we know S is short, so P is \(9-3=6\) and the rest are \(L\)