Mugs cost $6 and bowls cost $9. Ivy must spend at least $60. Can she… Step by Step

Step by step

The question

Question: Mugs cost $6 and bowls cost $9.

Ivy must spend at least $60.

Can she buy 0 mugs and 7 bowls?

1 Find what we know

What do we know?

Mugs cost $6 each.

Bowls cost $9 each.

Ivy must spend $60 or more.

What do we want?

To know if 0 mugs and 7 bowls fit.

2 Name the unknowns

We don't know how many mugs.

We call that number x.

x = number of mugs

We don't know how many bowls either.

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

y = number of bowls

3 Write the inequality

One mug costs $6.

So x mugs cost 6 times x: 6x.

x mugs: 6 × x = 6x

One bowl costs $9.

So y bowls cost 9 times y: 9y.

y bowls: 9 × y = 9y

At least $60 means $60 or more.

That is the sign more than or equal to.

at least $60 = $60 or more: ≥

In words: the mug money plus the bowl money is at least $60.

6x + 9y = 60

So the inequality is 6x + 9y ≥ 60.

6x + 9y ≥ 60

Careful!

At least means 60 or more.

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

Careful: not 6x + 9y ≤ 60 ✗

4 Put the point in

0 mugs: x = 0.

7 bowls: y = 7.

As a point, that is (0, 7).

x = 0 , y = 7 (0, 7)

We put them in.

Is it more than or equal to 60?

We don't know yet.

6 × 0 + 9 × 7 ≥? 60

6 times 0 is 0.

9 times 7 is 63.

6 × 0 = 0

9 × 7 = 63

0 plus 63 is 63.

0 + 63 ≥? 60

Is 63 more than or equal to 60?

Yes.

True!

63 ≥ 60 true

5 Answer the question

Yes: 0 mugs and 7 bowls cost $63.

6 Check

Let's check with the money.

That is $3 more than Ivy must spend.

So it is enough.

It works!

$63 − $60 = $3 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