New Math teacher thx to Rona... ugh

Question

At the local clothing store all shirts were on sale for one price and sweaters for a different price. Lonnie purchase three sweaters and two shirts for $130. If the sale price of the shirt was five dollars less than the sale price of a sweater, how much did each item cost Lonnie?

Answer 1

This is a systems of equations problem. I like to start all word problems by considering what information I am given and trying to form some equations. So, let's define some variables and start there.

S - sweater price

SH - shirt price

3*S + 2*SH = $130 This equation comes from the idea that they bought 3 sweaters and 2 shirts for $130.

S - $5 = SH This equation represents the idea that a shirt cost $5 less than a sweater.

Now we have two equations with two variables. The rules of algebra tell us that we need to have only one unknown variable in order to solve. We need to rewrite one equation in terms of the other in order to have only one unknown variable. The second equation tells us that we can substitute S-5 for SH in the first equation because SH = S - 5. This will allow us to solve for S and then use that information to solve for SH.

3*S + 2*SH = $130 (original equation)

3*S + 2*(S-5) = $130 (Substitute for SH)

3*S + 2S - 10 = $130 (Distribute the 2 through)

5S - 10 = $130 (Group like terms)

5S = $130 + 10 (Add 10 to both sides)

5S = $140 (Solve addition)

S = $28 (Divide both sides by 10)

Now we know that sweaters cost $28 each. We can use that information to find out how much shirts cost.

S - $5 = SH

$28 - $5 = SH

$23 = SH

Shirts cost $23 and sweaters cost $28.

Answer 2

Let x be the sale price of a shirt

and y be the sale price of a sweater

3y + 2x = 130

x = y - 5

Solve by simultaneous equation:

x = 23

y = 28