Ana has $50. She spends $6 a day. After how many days will she have… Step by Step

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The question

Question: Ana has $50.

She spends $6 a day.

After how many days will she have $8 left?

1 Find what we know

What do we know?

At the start: $50.

$6 for each day.

$8 is left at the end.

What do we want?

How many days.

2 Name the unknown

We don't know how many days.

So we call it x.

x = number of days

3 Write the equation

In words: the start, take away what is spent, leaves what is left.

50 − 6x = 8

So the equation is 50 − 6x = 8.

Now we solve it.

50 − 6x = 8

We want x by itself.

Two things are stuck to x: times −6 and + 50.

The + 50 is on the outside, so it comes off first.

Then the times −6.

4 Remove the 50

To remove 50, we take away 50.

We do it on both sides, so they stay equal.

50 − 6x ~~− 50~~ = 8 − 50

50 and − 50 make zero.

Cross them out.

8 − 50 = −42.

8 − 50 = −42

Now we have −6x = −42.

−6x = −42

5 Remove the −6

−6x means −6 times x.

We want just x.

To remove times −6, we divide by −6.

We do it on both sides, so they stay equal.

−6x−6 = −42−6

−6 divided by −6 is 1.

So just x is left.

−42 divided by −6 is 7.

−42−6 = 7

So x = 7!

x = 7

6 Answer the question

So the answer is 7 days.

7 Check

Let's check in the story.

7 days at $6 each: 7 times 6 is $42.

7 × $6 = $42

$50 take away $42 leaves $8, like the story says.

$50 − $42 = $8

Does it make sense?

A whole number of days.

And $8 left is less than the $50 at the start.

So the answer is right!

makes sense: 7 days: whole, $8 < $50

Let's look back.

First: find what we know.

Then: name the unknown.

Then: write the equation.

Then: solve it.

Then: answer the question.

Last: check.

Answer