Ali wants to save at least $90. He saves $12 each week. How many… Step by Step

Step by step

The question

Question: Ali wants to save at least $90.

He saves $12 each week.

How many weeks must he save?

1 Find what we know

What do we know?

At least $90.

$12 for each week.

What do we want?

How many weeks.

2 Name the unknown

We don't know how many weeks.

So we call it x.

x = number of weeks

At least $90 means $90 or more.

We write ≥ $90.

at least $90 → ≥ $90

3 Write the inequality

In words: what the weeks make is at least $90.

12x = 90

So the inequality is 12x ≥ 90.

Now we solve it.

12x ≥ 90

4 Remove the 12

12x means 12 times x.

We want just x.

To remove times 12, we divide by 12.

We do it on both sides, so the sign stays true.

12x12 ≥ 9012

12 divided by 12 is 1.

So just x is left.

We can make 90/12 simpler.

It is the same as 15/2.

9012 = 152

So x is greater than or equal to 15/2.

x ≥ 152

5 Show it on a number line

6 Answer the question

15/2 is 7.5.

152 = 7.5

Weeks come in whole numbers.

The smallest whole number from 7.5 up is 8.

So we round up.

x ≥ 8

Careful!

At least means we may not stop short.

So we always round up.

Careful: at least: round up

So at least 8 weeks.

7 Check

Let's check in the story.

8 weeks: $96.

That is at least $90.

8 weeks: 8 × $12 = $96 ≥ $90

But 7 weeks would be $84: not enough.

So 8 is the fewest.

So the answer is right!

7 weeks: 7 × $12 = $84 < $90 ✗

Let's look back.

First: find what we know.

Then: name the unknown.

Then: write the inequality.

Then: solve it.

Then: answer the question.

Last: check.

Answer