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By: awonder (offline)  Monday, February 22 2016 @ 01:56 AM CST (Read 916 times)  
awonder

Hi, need help on this question. TIA.

Prolly had 360 dolls more than Ariel at first. After Polly gave away 1/4 of her dolls and Ariel gave away 2/3 of her dolls, they had 764 dolls together. How many dolls did they give away altogether?

Please explain the steps and method use, thks.

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By: echeewh (offline)  Monday, February 22 2016 @ 08:38 PM CST  
echeewh

Hey <awonder>,

Appreciate you can also help provide answer key next time for easier verification.

Following is my worked solution:

<before>

P |---------|<- 360 ->|
A |---------|

<process>

P gave away (1/4)
A gave away (2/3)

From the equal qtys in the models of P, A above, split P into 4 parts and A into 3. As both have same qty, find lowest common multiple (LCM) of 4, 3 , i.e. 12.

Hence, <before>

P --> 12u + 360
A --> 12u

<after>

P --> (3/4) × (12u + 360) = 9u + 270
A --> (1/3) × (12u) = 4u

Given that there were 764 dolls left, we have ...

9u + 270 + 4u --> 764
13u --> 764 - 270 = 494
1u --> 494 ÷ 13 = 38

At first,

P --> 12u + 360
--> (12 × 38) + 360 = 816

A --> 12u
--> 12 × 38 = 456

Total (at first) = 816 + 456 = 1272

Total given away:

1272 - 764 = 508

======

Trust this helps.

Do let me know again if this is different from your <anskey> or if there's further clarification.

Cheers,
Edward

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Registered: 04/21/11
Posts: 627

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By: awonder (offline)  Tuesday, February 23 2016 @ 01:09 AM CST  
awonder

Thks Edward, yr working is very clear, appreciate your help.

Btw, the ans.. Is correct. My Daughter was asking why 270?

Quote by: echeewh

Hey <awonder>,

Appreciate you can also help provide answer key next time for easier verification.

Following is my worked solution:

<before>

P |---------|<- 360 ->|
A |---------|

<process>

P gave away (1/4)
A gave away (2/3)

From the equal qtys in the models of P, A above, split P into 4 parts and A into 3. As both have same qty, find lowest common multiple (LCM) of 4, 3 , i.e. 12.

Hence, <before>

P --> 12u + 360
A --> 12u

<after>

P --> (3/4) × (12u + 360) = 9u + 270
A --> (1/3) × (12u) = 4u

Given that there were 764 dolls left, we have ...

9u + 270 + 4u --> 764
13u --> 764 - 270 = 494
1u --> 494 ÷ 13 = 38

At first,

P --> 12u + 360
--> (12 × 38) + 360 = 816

A --> 12u
--> 12 × 38 = 456

Total (at first) = 816 + 456 = 1272

Total given away:

1272 - 764 = 508

======

Trust this helps.

Do let me know again if this is different from your <anskey> or if there's further clarification.

Cheers,
Edward

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Registered: 10/11/12
Posts: 4

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By: echeewh (offline)  Tuesday, February 23 2016 @ 02:12 AM CST  
echeewh

Hey <awonder>,

This number statement ..

P --> (3/4) × (12u + 360) = 9u + 270

is the same as follows:

[(3/4) × (12u)] + [(3/4) × (360)].

======

Trust this clarifies.

Cheers,
Edward

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Active Member

Registered: 04/21/11
Posts: 627

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