# Algebra approach to solving a word problem

#### Ibis

##### New member
Hi there,

This is my first time on this site. I do hope I'm submitting my question in the correct way.
Here is the question:

June spent 3/5 of her money in the first week and 1/3 of the remainder in the second week. She spent $110 altogether. How much money did she have left? I've solved the problem using Singapore Math styled model math. Not sure how to show my work using the model. But in the end I solved for 1/15 of the$110 and then 4/15. The answer is $40. I wanted to figure out how do solve it using algebraic equations instead of model math, but I can't seem to get it. Can you help me please? Ibis #### Subhotosh Khan ##### Super Moderator Staff member Hi there, This is my first time on this site. I do hope I'm submitting my question in the correct way. Here is the question: June spent 3/5 of her money in the first week and 1/3 of the remainder in the second week. She spent$110 altogether. How much money did she have left?

I've solved the problem using Singapore Math styled model math. Not sure how to show my work using the model. But in the end I solved for 1/15 of the $110 and then 4/15. The answer is$40.

I wanted to figure out how do solve it using algebraic equations instead of model math, but I can't seem to get it.

Ibis
How much money did she have left?
So we start with defining the unknown variable $$\displaystyle \to \ \ \$$money left = L

Also assume her starting money = S

Then:

June spent 3/5 of her money in the first week​

In first week she spent = 3/5 * S

Money left after first week = S - 3/5 * S = 2/5 * S

Then

She spent 1/3 of the remainder in the second week​

Money spent on second week = 1/3 * (2/5 * S) = 2/15 * S

So in combined two weeks she spent$$\displaystyle \to \ \ \$$ 3/5 * S + 2/15 * S = 11/15 *S

After two weeks, she would be left with $$\displaystyle \to \ \ \$$S - 11/15 *S = 4/15 * S

continue....

#### Jomo

##### Elite Member

So we start with defining the unknown variable $$\displaystyle \to \ \ \$$money left = L

Also assume her starting money = S

Then:

June spent 3/5 of her money in the first week​

In first week she spent = 3/5 * S

Money left after first week = S - 3/5 * S = 2/5 * S

Then

She spent 1/3 of the remainder in the second week​

Money spent on second week = 1/3 * (2/5 * S) = 2/15 * S

So in combined two weeks she spent$$\displaystyle \to \ \ \$$ 3/5 * S + 2/15 * S = 11/15 *S

After two weeks, she would be left with $$\displaystyle \to \ \ \$$S - 11/15 *S = 4/15 * S

continue....
I taught you well. It was only last year you asked basically this same question.

#### Ibis

##### New member

So we start with defining the unknown variable $$\displaystyle \to \ \ \$$money left = L

Also assume her starting money = S

Then:

June spent 3/5 of her money in the first week​

In first week she spent = 3/5 * S

Money left after first week = S - 3/5 * S = 2/5 * S

Then

She spent 1/3 of the remainder in the second week​

Money spent on second week = 1/3 * (2/5 * S) = 2/15 * S

So in combined two weeks she spent$$\displaystyle \to \ \ \$$ 3/5 * S + 2/15 * S = 11/15 *S

After two weeks, she would be left with $$\displaystyle \to \ \ \$$S - 11/15 *S = 4/15 * S

continue....
Just a quick note to say - thank you so much for taking the time to type up the solution so quickly.
If this was asked previously and answered my apologies. I did do a search prior to posting.

#### Subhotosh Khan

##### Super Moderator
Staff member
I taught you well. It was only last year you asked basically this same question.
Nope!!

Last year it was Gopal who spent the money - this year it was June who spent the money!

Totally different situation!!!