Hats cost $9 and gloves cost $14. Lily can spend at most $80. Can… Step by Step

Step by step

The question

Question: Hats cost $9 and gloves cost $14.

Lily can spend at most $80.

Can she buy 4 hats and 3 gloves?

1 Find what we know

What do we know?

Hats cost $9 each.

Gloves cost $14 each.

Lily can spend $80 or less.

What do we want?

To know if 4 hats and 3 gloves fit.

2 Name the unknowns

We don't know how many hats.

We call that number x.

x = number of hats

We don't know how many gloves either.

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

y = number of gloves

3 Write the inequality

One hat costs $9.

So x hats cost 9 times x: 9x.

x hats: 9 × x = 9x

One glove costs $14.

So y gloves cost 14 times y: 14y.

y gloves: 14 × y = 14y

At most $80 means $80 or less.

That is the sign less than or equal to.

at most $80 = $80 or less: ≤

In words: the hat money plus the glove money is at most $80.

9x + 14y = 80

So the inequality is 9x + 14y ≤ 80.

9x + 14y ≤ 80

Careful!

At most means 80 or less.

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

Careful: not 9x + 14y ≥ 80 ✗

4 Put the point in

4 hats: x = 4.

3 gloves: y = 3.

As a point, that is (4, 3).

x = 4 , y = 3 (4, 3)

We put them in.

Is it less than or equal to 80?

We don't know yet.

9 × 4 + 14 × 3 ≤? 80

9 times 4 is 36.

14 times 3 is 42.

9 × 4 = 36

14 × 3 = 42

36 plus 42 is 78.

36 + 42 ≤? 80

Is 78 less than or equal to 80?

Yes.

True!

78 ≤ 80 true

5 Answer the question

Yes: 4 hats and 3 gloves cost $78.

6 Check

Let's check with the money.

$2 is left, not below 0.

So Lily can pay.

It works!

$80 − $78 = $2 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