Bags cost $25 and belts cost $15. Tom can spend at most $120. Can he… Step by Step

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The question

Question: Bags cost $25 and belts cost $15.

Tom can spend at most $120.

Can he buy 3 bags and 3 belts?

1 Find what we know

What do we know?

Bags cost $25 each.

Belts cost $15 each.

Tom can spend $120 or less.

What do we want?

To know if 3 bags and 3 belts fit.

2 Name the unknowns

We don't know how many bags.

We call that number x.

x = number of bags

We don't know how many belts either.

It is a different number, so it gets its own letter: y.

y = number of belts

3 Write the inequality

One bag costs $25.

So x bags cost 25 times x: 25x.

x bags: 25 × x = 25x

One belt costs $15.

So y belts cost 15 times y: 15y.

y belts: 15 × y = 15y

At most $120 means $120 or less.

That is the sign less than or equal to.

at most $120 = $120 or less: ≤

In words: the bag money plus the belt money is at most $120.

25x + 15y = 120

So the inequality is 25x + 15y ≤ 120.

25x + 15y ≤ 120

Careful!

At most means 120 or less.

So the sign is less than or equal to, not more than.

Careful: not 25x + 15y ≥ 120 ✗

4 Put the point in

3 bags: x = 3.

3 belts: y = 3.

As a point, that is (3, 3).

x = 3 , y = 3 (3, 3)

We put them in.

Is it less than or equal to 120?

We don't know yet.

25 × 3 + 15 × 3 ≤? 120

25 times 3 is 75.

15 times 3 is 45.

25 × 3 = 75

15 × 3 = 45

75 plus 45 is 120.

75 + 45 ≤? 120

Is 120 less than or equal to 120?

Yes.

True!

120 ≤ 120 true

5 Answer the question

Yes: 3 bags and 3 belts cost $120.

6 Check

Let's check with the money.

$0 is left, not below 0.

So Tom can pay.

It works!

$120 − $120 = $0 left

Let's look back.

First: find what we know.

Then: name the unknowns.

Then: write the inequality.

Then: put the point in.

Then: answer the question.

Last: check.

Answer