How much more money?
The ratio of Beatriz’s savings to Hannah’s savings is 4 : 7. The ratio of Hannah’s savings to Julia’s savings is 3 : 5. The three girls have a total savings of $136. How much more money has Julia saved than Beatriz? Explain how you got your answer.
http://www.jiskha.com/display.cgi?id=1418686245
To find out how much more money Julia has saved than Beatriz, we need to determine the individual savings of each girl first.
Let's assume Beatriz's savings as 4x, where x represents the common ratio between their savings.
According to the given ratio, Hannah's savings would be 7x.
Then, since we already know the total savings of the three girls is $136, we can set up the equation:
Beatriz's savings (4x) + Hannah's savings (7x) + Julia's savings = $136
Combining like terms, we get:
11x + Julia's savings = $136
Now, let's consider the ratio between Hannah's savings (7x) and Julia's savings. It is given as 3 : 5, which can be represented as:
7x / Julia's savings = 3/5
To solve for the value of Julia's savings, we can cross-multiply:
7x * 5 = 3 * Julia's savings
35x = 3 * Julia's savings
Julia's savings = 35x / 3
Substituting this value into the previous equation, we can solve for x:
11x + (35x / 3) = $136
Multiplying through by 3 to eliminate the fraction:
33x + 35x = $408
68x = $408
Dividing both sides by 68:
x = $6
Now, we can find Beatriz's savings by substituting x = $6 into the equation:
Beatriz's savings = 4x
= 4 * $6
= $24
And we can find Julia's savings by substituting x = $6 into the equation:
Julia's savings = 35x / 3
= 35 * $6 / 3
= $70
Finally, to determine how much more money Julia has saved than Beatriz, we subtract Beatriz's savings from Julia's savings:
Julia's savings - Beatriz's savings
= $70 - $24
= $46
Therefore, Julia has saved $46 more than Beatriz.
To find out how much more money Julia has saved than Beatriz, we first need to calculate the individual savings of each girl.
Let's denote Beatriz's savings as 4x, Hannah's savings as 7x, and Julia's savings as 5y (y is a scaling factor).
According to the given ratios, we know that:
(1) Beatriz's savings to Hannah's savings is 4 : 7
-> 4x / 7x = 4/7
(2) Hannah's savings to Julia's savings is 3 : 5
-> 7x / 5y = 3/5
Next, we can use the total savings information to solve for x and y.
The total savings of the three girls is $136.
So, the sum of their individual savings is:
4x + 7x + 5y = 136
Combining like terms, we have:
11x + 5y = 136
Using equations (1) and (2), we can eliminate y and solve for x:
(1) 4x / 7x = 4/7
Cross multiplying, we get:
7(4x) = 4(7x)
28x = 28x
(2) 7x / 5y = 3/5
Cross multiplying, we get:
5(7x) = 3(5y)
35x = 15y
From equation (2), we can rewrite it as y = (35x)/15 = (7x)/3
Substituting this value of y into the equation 11x + 5y = 136, we have:
11x + 5((7x)/3) = 136
Multiplying through by 3 to eliminate the fraction, we get:
33x + 35x = 408
68x = 408
Dividing by 68, we find:
x = 6
Now that we know x = 6, we can substitute it back into equation (1) to get Beatriz's savings:
4x = 4(6) = 24
Therefore, Beatriz's savings are $24.
To find Julia's savings, we substitute x = 6 into y = (7x)/3:
y = (7(6))/3 = 14
Julia's savings are $14.
Finally, to calculate how much more money Julia has saved than Beatriz, we subtract Beatriz's savings from Julia's savings:
Julia's savings - Beatriz's savings = 14 - 24 = -$10
Julia has saved $10 less than Beatriz.
Therefore, the answer is that Julia has saved $10 less than Beatriz.