Question

Jolene spent ¼ of her salary on a bag. She bought a pair of shoes with 1/6 of the remaining money and a scarf with \$225. She then gave 2/5 of the rest of her money to her mother and \$180 to her son. In the end, she had 3/10 of her salary left. How much was Jolene’s salary

Hi ,

I do not understand the part of

after giving 2/5 to her mum     5/3x(3u = 180)

where does the 5/3 come from?

thank you for helping

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Hi chloecube, further to what Ender explained, you can refer to steps #2a to #2b to #2c of the branch diagram I tagged in BigDevil’s solution below.

I used to explain to my nephew this way. Look at 1/5 , 3/5 and 5/5 as pizza slices.

1 whole pizza is cut into 5 slices –> 1/5 is 1 slice  –>  3/5 is 3 slices –> So 5/5 is 5 slices of pizza or get back 1 whole pizza.

Each of us here has our own way to derive back the amount for 5/5, given that we know 3/5 is 3u+180. Essentially it is the same thing:

(a) x 5/3 (Siglapmaths’ working)

(b) divide by 3/5 (Ender’s explanation)*

(c) over 3, then x 5 (BigDevil’s working)

(d) divide by 3 to find 1/5, then times 5 to find 5/5 (My “pizza slices”)

Find one method that suits you, but most importantly, gain understanding and internalise that each is the same.

yes thank you so much all 🙂

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3u + 180 is 3/5 of the money before she gave to her mom.

So to find out the amount of money before she gave to her mom, which is 5/5, we divide (3u + 180) by 3/5. Which is the same as multiplying by 5/3.

For visual representation, take a look at  Bigdevil’s solution. 3rd row from the top is a 5 box model representing the amount money before she gave her mother. Where 3 of the boxes representing 3u +180.

That step you are asking is to find out what is the amount of money before she gave her mother, which is all the 5  boxes.  Which is (3u +180) divide by 3/5.

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Hi BigDevil, don’t mind I tag a branch diagram here since it is your solution.

Be my guest, SAHMom. Anything to help the kids understand.  😎

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Thank you all for your quick solutions.

Really appreciate all the response.

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Thank you all for your quick solutions.

Really appreciate it.

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I have solved the above question as follows :

salary ——- 40u
(1/4) x 40u = 10u (bag)
40u – 10u = 30u
(1/6) x 30u = 5u (shoes)
225 (scarf)
2/5 of the rest of her money (mother)
180 (son)
(3/10) x 40 = 12u (left)
3/5 of the rest of her money ——- 180 + 12 u
1/5 of the rest of her money ——- 60 + 4u
5/5 of the rest of her money ——- 300 + 20u
300 + 20u + 225 ——- 40u – 10u – 5u = 25u
1u ——- (300 + 225)/5 = 105
40u ——- 105 x 40 = 4200

Ans : \$4200.

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If a branch diagram helps. I think this is the most complex level of branch diagram I have drawn so far. BigDevil has done working backwards, my branch diagram is “top down” approach.

See last bracket:   9u-315 = 3 parts of Salary

1 part of Salary = 3u-105

10 parts of Salary = 30u-1050 = 24u (also Whole Salary)

u = 175

Salary = 24u = \$4200#

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