SOLUTION: Hi Iris jolene and Karen bought a gift. They shared the cost among themselves. Iris and jolene made up 3/5 of the sum of money. Iris and Karen made up 13/20 of the sum of money. J

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Question 1207651: Hi
Iris jolene and Karen bought a gift. They shared the cost among themselves. Iris and jolene made up 3/5 of the sum of money. Iris and Karen made up 13/20 of the sum of money. Jolene and Karen paid $195 altogether. How much more money did jolene pay than Iris.

Found 4 solutions by josgarithmetic, greenestamps, math_tutor2020, Edwin McCravy:
Answer by josgarithmetic(39626)   (Show Source): You can put this solution on YOUR website!
               sent.2       sent.3           sent. 2&3
Iris              i           i               i
Jolene            j           7g/20          7g/20
Karen            2g/5         k              2g/5
TOTAL              g          g               g

Sentence 4 means that ; not yet the answer to the question but
solving for g will allow to find all the unknown quantities.

k is in terms of g
j is in terms of g






=========================
Jolene paid 91 dollars.
Karen paid 104 dollars.
=========================



Iris paid 65 dollars.

How much more Jolene than Iris?
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


Let I, J, and K represent the amounts Iris, Jolene, and Karen contributed, respectively.

Let x be the total cost.

Then....

I+J = (3/5)x
I+K = (13/20)x

Add the two equations:

2I+J+K= (3/5)x + (13/20)x = (12/20)x + (13/20)x = (25/20)x = (5/4)x

But

I+J+K = x

so

I = (2I+J+K)-(I+J+K) = (5/4)x-x = (1/4)x

So Iris paid 1/4 of the total, which means Jolene and Karen together paid 3/4 of the total. Jolene and Karen together spent $195:

(3/4)x = 195
x = 195*(4/3) = 260

The total cost was $260.

So the amount Iris paid was 1/4 of $260, or $65.

Iris and Karen together paid 13/20 of the total; Iris and Jolene together paid 3/5 of the total. The difference between those amounts is the difference between what Karen paid and what Jolene paid:

I+K = (13/20)x
I+J = (12/20)x
K-J = (I+K) - (I+J) = (1/20)x

Karen spent (1/20)x = $13 more than Jolene; and together the two of them spent $195. Use formal algebra or informal logical reasoning and simple arithmetic to determine that Karen spent $104 and Jolene spent $91.

Now we have the amounts that each of them spent:

Iris: $65
Jolene: $91
Karen: $104

ANSWER: Jolene spent $91-$65 = $26 more than Iris.
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answer: $26


Explanation

i,j,k = iris, jolene, karen
i+j+k = x = total cost
3/5 = 12/20

Based on the info given, we can form these three equations
i+j = (12/20)x
i+k = (13/20)x
j+k = 195

Add them up to get
(i+j)+(i+k)+(j+k) = (12/20)x+(13/20)x+195
2(i+j+k) = (25/20)x+195
2x = (5/4)x+195
4*2x = 4*( (5/4)x+195 )
8x = 5x+780
8x-5x = 780
3x = 780
x = 780/3
x = 260 is the total

We want to know how much more Jolene paid compared to Iris.
Therefore we wish to determine the value of j-i
Refer to the system of equations mentioned above. Let's subtract equations (3) and (2) in that order.

(j+k)-(i+k) = 195 - (13/20)x
j+k-i-k = 195 - (13/20)*260
j-i = 26 is the final answer

j-i = 26 rearranges to j = i+26 to indicate that whatever Iris paid, Jolene paid $26 more.
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Let T = the total price of the gift and M = How much more money Jolene paid 
than Iris.



Put those equations in an online solver and instantly get

J = 91, K = 104, I = 65, M = 26, T = 260

The answer is M = 26

[These days, there are online solvers for almost anything in mathematics.] 

Edwin
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