The cost of a shirt is $3 more than half the price of a pair of jeans. The cost of the shirt and jeans together is $45. Find the cost of each item.

Question

OK, so I really struggle with math and I was hoping someone could help or explain this to me. And since I'm also in grade 9, we only use one variable.

When I tried it my equation ended up being x+(x÷2 [as a fraction] +3) but when I solved it I got $42. If you can help me that would be great!

Answer 1

Translation is the harder part. We will get to your equation as follows:

First identify all the quantities involved (even though it’s more than one; bear with me)

Let S be the cost of a shirt.

Let J be the cost of jeans.

Now Translate the words into equations:

Translate “the cost of a shirt“ into “S”.

Translate “is 3 more than half the price of jeans” Into “= 3 + J/2”

Put them together:

S= 3 + J/2

 

Now, Translate “the cost of jeans and shirt is $45” into “J + S = 45”

 

so So you have two equations, and two variables. That’s life! But it’s easy to simplify. You have an equation giving a formula for S, so replace “S” with “(3 + J/2)” in the equation with 45 in it.

 

j + (3+ J/2) = 45

 

now you have one equation and one variable. Solve it, and you’ll have the price of jeans.

 

subtract that from 45, and you’ll have the price of a shirt.