Pencils cost $2 and markers cost $3. Zoe must spend at least $25… Step by Step

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The question

Question: Pencils cost $2 and markers cost $3.

Zoe must spend at least $25.

Can she buy 4 pencils and 6 markers?

1 Find what we know

What do we know?

Pencils cost $2 each.

Markers cost $3 each.

Zoe must spend $25 or more.

What do we want?

To know if 4 pencils and 6 markers fit.

2 Name the unknowns

We don't know how many pencils.

We call that number x.

x = number of pencils

We don't know how many markers either.

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

y = number of markers

3 Write the inequality

One pencil costs $2.

So x pencils cost 2 times x: 2x.

x pencils: 2 × x = 2x

One marker costs $3.

So y markers cost 3 times y: 3y.

y markers: 3 × y = 3y

At least $25 means $25 or more.

That is the sign more than or equal to.

at least $25 = $25 or more: ≥

In words: the pencil money plus the marker money is at least $25.

2x + 3y = 25

So the inequality is 2x + 3y ≥ 25.

2x + 3y ≥ 25

Careful!

At least means 25 or more.

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

Careful: not 2x + 3y ≤ 25 ✗

4 Put the point in

4 pencils: x = 4.

6 markers: y = 6.

As a point, that is (4, 6).

x = 4 , y = 6 (4, 6)

We put them in.

Is it more than or equal to 25?

We don't know yet.

2 × 4 + 3 × 6 ≥? 25

2 times 4 is 8.

3 times 6 is 18.

2 × 4 = 8

3 × 6 = 18

8 plus 18 is 26.

8 + 18 ≥? 25

Is 26 more than or equal to 25?

Yes.

True!

26 ≥ 25 true

5 Answer the question

Yes: 4 pencils and 6 markers cost $26.

6 Check

Let's check with the money.

That is $1 more than Zoe must spend.

So it is enough.

It works!

$26 − $25 = $1 more than needed

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