Challenging Word Problem

Question

If Vivian gives $2.20 to Jennifer, she will have three times as much money as Jennifer. If Vivian gives $5.80 to Jennifer, she will have twice as much money as Jennifer. How much money does Vivian have?

Answer 1

Hi Jody,

Question: If Vivian gives $2.20 to Jennifer, she will have three times as much money as Jennifer. If Vivian gives $5.80 to Jennifer, she will have twice as much money as Jennifer. How much money does Vivian have?

Given:

1) If Vivian give 2.20 to Jennifer Vivian will have 3x as much as Jennifer

2) If Vivian give 5.80 to Jennifer Vivian will have 2x as much as Jennifer

Find:

How much money does Vivian have?

Looking at this problem I see they gave me two scenarios where Vivian gives different amounts of money. There are 2 people involved. So that it seeming to me like we are talking about 2 unknows Vivian and Jennifer. To find their values, I need to generate 2 equations.

Let v = amount of money Vivian has

Let j = amount of money Jennifer has

1) If Vivian give 2.20 to Jennifer Vivian will have 3x as much as Jennifer

Vivian gives.. So we are subtracting from Vivian v-2.20

will have .. that means "="

3x as much as Jennifer.. 3j

v-2.20 = 3j

2) If Vivian give 5.80 to Jennifer Vivian will have 2x as much as Jennifer

v-5.80 = 2j

Now you have a 2 equations and 2 unknowns and you can solve by the method of your choice.

I'll do substitution

v-2.20 = 3j

v= 3j+2.20

v-5.80=2j

(3j+2.20) - 5.80 = 2j

3j -3.6 = 2j

j = 3.6

v= 3j+2.20

v = 3(3.6) + 2.20

v = 13

Check and confirm works for both equations

v-5.80 = 2j

13-5.80 ?= 2(3.6)

7.2 ?= 7.2 yes works

v-2.20 = 3j

13-2.2 ?= 3(3.6)

10.8 ?= 10.8 Yes it works

SO v=13 and j = 3.6

Hope this helps