(Easy?) Maths Question?

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?)

Answer 1

Its a problem that can be solved with algebra, but if you don't know algebra it can be solved by just logic.

Working backwards from the end, he ended up with 1/8 of his total pocket money after spending 3/4 on his phone bill. So before he paid the phone bill he had 4/8 of his total pocket money left, or 1/2. If he had 1/2 left after spending $160 on food, then $160 was the other half, so he started out with 2x $160, or $320.

I always liked story problems, and this one is pretty simple, but I'm not sure I could have done it myself when I was 9.

Answer 2

First of all try writing MATH and leaving off the s. Say "math question". now say "mathS question". Can you honestly say that that sounds good? Do you actually pronounce the "s" at the end when you say it out loud? Do you? I know the British do that "s" stuff but so what?

Anyway, onto the problem.

P = total pocket money
Total spent: S = 160 + (3/4)(P - 160)
P - S = P/8 ...... He has 1/8 of his pocket money left
P - (160 + 3P/4 - 120) = P/8 = P - (40 + 3P/4 ) = 2P/8 = 40
P/8 = 40
And P = 320 (I always like to put in enough information so everything is, I hope, clearly visible)

As to whether or not this is too difficult for a 9 year old, I shall paraphrase from a Sherlock Holmes movie since I don't remember exactly what Watson said:

Watson: "So easy a child could do it."
Holmes: "Not your child Watson."

Answer 3

In the end, there's 1/8 of the total left, but it's also 1/4 of the ramaining money after he has spent on food (because 3/4 of the remaining money has been spent to pay the bill). So both the money spent on food and the remaining money makes up 1/2 of the total --> the total is 320.

Answer 4

The way to solve this type of question is to translate the problem into an equation, then solve the equation using the usual rules of algebra.

Start by giving required solution a symbol. p= pocket money.

then write down what you know about p, finding the info in the question. The pocket money is made up from the sum of certain quantities, money spent on food, phone bill, money left over, etc -

p= 160 + 0.75(p-160) +p/8

now solve the equation -

Multiply through by 8
8p = 160*8 + 6p - 160*6 +p

Separate p quantities and numerical values
8p-6p-p = 160*2

Add it all up
p= $320

I hope that helps.....

Answer 5

Initial money Denis has is X

So after doing first transaction remaining balance is X-160(assume this as Y)

Now after 2nd Transaction i.e. 3/4th of the remaining amount the balance is
Y-3Y/4---- 1

which is then equal to X/8---- 2

now equate 1 and 2 we get

Y-3Y/4 = X/8---3

replace Y then we get
(X-160) - 3(X-160)4 = X/8 and solve the eqn for X we get X=320

Answer 6

x - 160 - (3/4)(x - 160) = x/8
Multiplying by 8,
8x - 1,280 - 6(x - 160) = x
Distributing the - 6,
8x - 1,280 - 6x + 960 = x
Grouping the LHS,
2x - 320 = x
Subtracting x
x - 320 = 0
Adding 320,
x = 320

Answer 7

x - pocket money
$160 - spend on food
(3/4)(x-160) - mobile phone bill
x/8 - left

x - 160 - [(3/4)(x-160)] = x/8
x - 160 - [( 3x - 480)/4] = x/8
8{x - 160 - [(3x-480)/4]} = x
8x - 1280 - 2(3x - 480) = x
8x - 1280 - 6x + 960 = x
2x - 320 = x
------------> x = 320

Answer 8

14 + 12 + 5 = 31 so 2 scholars are donning the two a) 14+12-2 = 24 b) 14-2 = 12 c) 12-2 = 10 Please notice that alot of folk will answer 26 for the 1st question, even nonetheless that's faulty: 29 - 5 = 24 (minus of folk who arent donning pink OR blue 14+12 = 26 there is 26 blue and pink colorings yet in basic terms 24 scholars this suggests 2 human beings might desire to be donning the two colorings as I in basic terms stated there is in basic terms 24 human beings so what proportion pink and blue = 24 pink no longer blue = pink human beings much less the persons who donning the two blue no longer pink = blue human beings much less the persons who donning the two

Answer 9

x=160 + (x-160)*3/4+x/8
x=160+3/4x-120+x/8
x-3/4x-x/8=40
(8x-6x-x)/8=40
x/8=40
x=320

Answer 10

Let x = money Denis had at first.

Equation:
x - $160.00 - (3/4[x - $160.00]) = 1/8x
x - $160.00 - (3/4x - $120.00) = 1/8x
x - $160.00 - 3/4x + $120.00 = 1/8x
1/4x - $40.00 = 1/8x
1/4x - 1/8x = $40.00
2/8x - 1/8x = $40.00
1/8x = $40.00
x = $40.00 / (1/8)
x = $40.00 * 8/1
x = $320.00

Answer: Denis had $320.00 at first.

Proof:
$320.00 - $160.00 - (3/4[$320 - $160.00]) = 1/8($320.00)
$160.000 - ($240.00 - $120.00) = $40.00
$160.00 - $120.00 = $40.00
$40.00 = $40.00