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 By: adilah9 (offline)  Saturday, February 04 2012 @ 10:25 PM CST (Read 1611 times)

If Juno give \$25 to Leon, he will have four times as much money as Leon.
If Juno gives \$69 to Leon, he will have twice as much money as him.

(a) How much money does Juno have?
(b) How much money do Juno and Leon have altogether?

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Registered: 09/19/11
Posts: 12

 By: awyw1201 (offline)  Sunday, February 05 2012 @ 06:32 AM CST
awyw1201

If Juno give \$25 to Leon, he will have four times as much money as Leon.
If Juno gives \$69 to Leon, he will have twice as much money as him.

(a) How much money does Juno have?
(b) How much money do Juno and Leon have altogether?

Let the amount of money Leon has be 1u.

If Juno gives \$25 to Leon,

Leon---1u + 25
Juno----(1u +25) x 4 = 4u + 100----(1)

If Juno gives \$69 to Leon,

Leon---1u +69
Juno --- (1u + 69) x 2 = 2u + 138----(2)

(1) must be equal to (2), thus
4u + 100 = 2u + 138
2u= 38
1u = 19 (Leon)
Juno---(19 + 69) x2 + 69 = 245
Both----245 + 19 = 264

Ans: (a) \$245 (b) \$264

Regular Member

Registered: 07/08/11
Posts: 87

 By: adilah9 (offline)  Sunday, February 05 2012 @ 07:05 AM CST

Quote by: awyw1201

If Juno give \$25 to Leon, he will have four times as much money as Leon.
If Juno gives \$69 to Leon, he will have twice as much money as him.

(a) How much money does Juno have?
(b) How much money do Juno and Leon have altogether?

Let the amount of money Leon has be 1u.

If Juno gives \$25 to Leon,

Leon---1u + 25
Juno----(1u +25) x 4 = 4u + 100----(1)

If Juno gives \$69 to Leon,

Leon---1u +69
Juno --- (1u + 69) x 2 = 2u + 138----(2)

(1) must be equal to (2), thus
4u + 100 = 2u + 138
2u= 38
1u = 19 (Leon)
Juno---(19 + 69) x2 + 69 = 245
Both----245 + 19 = 264

Ans: (a) \$245 (b) \$264

Thank you once again

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Registered: 09/19/11
Posts: 12

 By: josephine_ng (offline)  Sunday, February 05 2012 @ 11:57 PM CST
josephine_ng

If Juno has \$245 and Leon has \$19,

after Juno gives Leon \$25, it'll be J-\$220 and L-\$44.

That isn't 4 times, it's 5 times.

How come (1) and (2) is the same? If juno gives more, than the previous time, she shouldn't have the same amount as the previous time but has lesser.

My take:
Draw 'give \$25' model - J (4U), L (1U) = Total 5U
Draw 'give \$69' model - J (2U), L (1U) = Total 3U

Since it's internal transfer whereby the total number do not change, the total units (15U-common multiple) shouldn't change as well.
Therefore, cut each unit in the 'GIVE \$25' model into 3 parts each unit and cut each unit in the 'GIVE \$69' model into 5 parts each unit.

You should get 15 parts in each model.

Look at leon, there's a difference in the 'give \$25' model and 'give \$69 model' of 2 parts.

There's a difference of 2 parts because he received \$46 on the 2nd model.

Therefore, based on 'give \$25' model,

2 parts = \$46
1 part = \$46 / 2 = \$23
12 parts = \$23 x 12 = \$276
15 parts = \$23 x 15 = \$345

Juno = \$276 + \$25 = \$301 ----- (a)

**work backwards to check, juno should get 4 times of leon if she gives him \$25**
**alternatively, depending on student's preference, you may use ratio method, applying the same logic that the total number of units doesn't change.**

eg, 4 : 1 , 2 : 1
12 : 3 , 10 : 5
12 - 10 = 2
or
5 - 3 = 2

2 units = \$69 - \$25= \$46

Newbie

Registered: 02/05/12
Posts: 2

 By: awyw1201 (offline)  Monday, February 06 2012 @ 12:34 AM CST
awyw1201

Quote by: josephine_ng

If Juno has \$245 and Leon has \$19,

after Juno gives Leon \$25, it'll be J-\$220 and L-\$44.

That isn't 4 times, it's 5 times.

How come (1) and (2) is the same? If juno gives more, than the previous time, she shouldn't have the same amount as the previous time but has lesser.

My take:
Draw 'give \$25' model - J (4U), L (1U) = Total 5U
Draw 'give \$69' model - J (2U), L (1U) = Total 3U

Since it's internal transfer whereby the total number do not change, the total units (15U-common multiple) shouldn't change as well.
Therefore, cut each unit in the 'GIVE \$25' model into 3 parts each unit and cut each unit in the 'GIVE \$69' model into 5 parts each unit.

You should get 15 parts in each model.

Look at leon, there's a difference in the 'give \$25' model and 'give \$69 model' of 2 parts.

There's a difference of 2 parts because he received \$46 on the 2nd model.

Therefore, based on 'give \$25' model,

2 parts = \$46
1 part = \$46 / 2 = \$23
12 parts = \$23 x 12 = \$276
15 parts = \$23 x 15 = \$345

Juno = \$276 + \$25 = \$301 ----- (a)

**work backwards to check, juno should get 4 times of leon if she gives him \$25**
**alternatively, depending on student's preference, you may use ratio method, applying the same logic that the total number of units doesn't change.**

eg, 4 : 1 , 2 : 1
12 : 3 , 10 : 5
12 - 10 = 2
or
5 - 3 = 2

2 units = \$69 - \$25= \$46

Hi, Josephine. I agree with u. Sorry i think i made a mistake when i check the answers.

Regular Member

Registered: 07/08/11
Posts: 87

 By: awyw1201 (offline)  Monday, February 06 2012 @ 12:42 AM CST
awyw1201

(a) \$289
(b) \$330

Regular Member

Registered: 07/08/11
Posts: 87

 By: awyw1201 (offline)  Monday, February 06 2012 @ 12:51 AM CST
awyw1201

Quote by: josephine_ng

If Juno has \$245 and Leon has \$19,

after Juno gives Leon \$25, it'll be J-\$220 and L-\$44.

That isn't 4 times, it's 5 times.

How come (1) and (2) is the same? If juno gives more, than the previous time, she shouldn't have the same amount as the previous time but has lesser.

My take:
Draw 'give \$25' model - J (4U), L (1U) = Total 5U
Draw 'give \$69' model - J (2U), L (1U) = Total 3U

Since it's internal transfer whereby the total number do not change, the total units (15U-common multiple) shouldn't change as well.
Therefore, cut each unit in the 'GIVE \$25' model into 3 parts each unit and cut each unit in the 'GIVE \$69' model into 5 parts each unit.

You should get 15 parts in each model.

Look at leon, there's a difference in the 'give \$25' model and 'give \$69 model' of 2 parts.

There's a difference of 2 parts because he received \$46 on the 2nd model.

Therefore, based on 'give \$25' model,

2 parts = \$46
1 part = \$46 / 2 = \$23
12 parts = \$23 x 12 = \$276
15 parts = \$23 x 15 = \$345

Juno = \$276 + \$25 = \$301 ----- (a)

**work backwards to check, juno should get 4 times of leon if she gives him \$25**
**alternatively, depending on student's preference, you may use ratio method, applying the same logic that the total number of units doesn't change.**

eg, 4 : 1 , 2 : 1
12 : 3 , 10 : 5
12 - 10 = 2
or
5 - 3 = 2

2 units = \$69 - \$25= \$46

Hi,
i think 2 units =\$69 - \$25 = \$44, (not \$46)
Thus, 1 unit = 22

(a) Juno---22 x 12 + 25 = 289, (not 301)
(b) 22 x 15 = 330

Am i right?

Regular Member

Registered: 07/08/11
Posts: 87

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