Question

Nathan buys 15 articles of clothing (shirts and pants) at a local clothing store during a big sale. Each shirt (s) costs $3.00 and each pair of pants (p) costs $10.00. The total amount he spends (before tax) is $94. If you want to know how many shirts and pairs of pants he bought, what matrix equation could you write to solve?
A)

1 1
3 10

s
p

=

15
94

B)

1 3
1 10

s
p

=

15
94

C)

15 3
10 94

s
p

=

1
1

D)

3 10
15 94

s
p

=

1
1

Answer 1

before writing the matrix equation, start with a regular equation

let s = # of shirts
let p = # of pants

if the total # of items is 15, then s + p = 15

the amount spent on shirts is (price per shirt)(number of shirts), or 3.00s after filling in the appropriate information from the problem

same logic w/ the pants

add up shirt and pant cost, and set that equal to the total cost (94). that'll give you your second equation.

Answer 2

put them together, that's your system. now, to translate this into a matrix equation, take the coefficients and place them into the leftmost 2x2 matrix. the variables go into the second, 2x1 matrix. finally, the constants go into the last 2x1 matrix