**Question:**hi all, this question is actually in one of the exam practise papers for my younger brother who's only 9. I don't know if i should be worried but i came up with the answer (320) using a 6-step long algebraic method.

As i am tutoring him, do any of you guys know an easier, simpler, way to solve it so i can help him understand better? He hasn't learnt algebra yet.

Here's the question:

"After Denis spent $160 of his pocket money on food, and 3/4 of the remaining money to pay his mobile phone bill, he had 1/8 of his total pocket money left. How much pocket money did Denis have at first?"

Thank you so much! Also just out of curiosity, does anyone else think this maths problem isn't so easy for a 9 year old? (or am i just a little daft?)

**Answers:**

I tried it like five different ways that I've learned, and none of them worked.

But in the equations that other people posted I'm not quite getting how 7/8-3/4=160.

I set it up as :

3/4(x-160)=1/8x

But it didn't work...

I agree, it's too hard for a 9 year old, especially if they didn't teach him how to do it...

------------------------------...

I just read through the two above me and I don't think either of them realized that it's supposed to be 3/4 of the remaining money, not that he spent 3/4 of the total money. How else would he have 1/8 left?

Dude, I'm not even doing that and I'm 13.

I know, I'm extremely stupid with math.

The amount of money he spent: 1-1/8=7/8

How much in fraction is $160 in the money he spent: 7/8-3/4=$160

7/8-6/8=$160

1/8=$160

$160 divide 1/8= $160*8=$1280

So the answer is $1280.

No, it's easy for a 9 year old. Well, it is in my country.

Hi, whether you’re 9 or 19, these questions can be a little tricky to set up. In these kinds of problems we are looking to find a variable (an unknown) usually marked by the letter “x”. Then you explain to your brother that in order to solve for “x” we need to set up an equation. Having said these, let’s take a look at your question:

Denis was left at the end with 1/8 of his money We want to see how much he had spent. . (8/8 X) is the same as one X. we use the expression 8/8 instead of the number 1 because 8 divided by 8 is 1 and it just helps us in solving the fraction. That means if “x” was all his money, he must have spent 7/8 of it to be left with 1/8 or mathematically 8/8X-1/8X = 7/8X

7/8X is going to be the left portion of our equation.. Great.. We are half way done. Now comes the part that needs a little practice to get it easier. We need to express the 7/8 in a mathematical way meaning. What is this 7/8 in term of ‘x’ and numbers.

We know 2 things:

1) he spent $160 on food so we have on the right side of the equation the value “160”

2) Also on the right side of the equation we say that if the variable “X” is all his money, then he spent ¾ of it, which means he spent ¾ x

Knowing these 2 facts we can now build our equation which is the following:

7/8 X = 160 + ¾ X

To solve for “X” in this equation you moved the X variables to the left of the = and the numbers on the right, so re-write this equation as: (don’t forge to change the signs when moving from one side of the equation to the other :)

7/8X – ¾ X = 160

If you multiply ¾ by 2/2 which is 1 and doesn’t change the value any, it just makes the fraction subtraction easier you will get:

7/8X -6/8X =160

This gives you

1/8X =160

Finally multiplying 160 with 8 with give you the answer.

X = 160*8

X= 1280

Your teacher might be a little tough, most math teachers are so don’t forget to put the unit for 1280 which is in dollars $. So your answer is

$1280

Good luck to you and your brother :)

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