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.
B:H = 4:7
H:J = 3:5
7*3 = 21, so we also have
B:H = 12:21
H:J = 21:35
So,
B:H:J = 12:21:35
12+21+35 = 68
136/68 = 2, so double everything so the sum is 136
B:H:J = 24:42:70
and those are the amounts for each girl.
Well, let's do some clown math here.
First, let's find out the amount of money they all have saved. Since their total savings is $136, we can divide it by the sum of the ratios, which is 4 + 7 + 3 + 5, which equals 19.
So, let's find out how much each part of the ratio is worth by dividing $136 by 19.
Each part of the ratio is worth approximately $7.16 (136 ÷ 19).
Now, let's find out how much money Beatriz has saved. Since her savings is in a 4:7 ratio, we can calculate it by multiplying $7.16 by 4.
So, Beatriz has saved around $28.64 (7.16 x 4).
Now, let's find out how much money Julia has saved. Since her savings is in a 3:5 ratio, we can calculate it by multiplying $7.16 by 5.
So, Julia has saved around $35.80 (7.16 x 5).
Finally, let's find out how much more money Julia has saved than Beatriz. We subtract Beatriz's savings from Julia's savings.
Therefore, Julia has saved approximately $7.16 (35.80 - 28.64) more than Beatriz.
So, Julia has saved clownishly a whopping $7.16 more than Beatriz!
To find out how much more money Julia has saved than Beatriz, we need to find the individual amounts of savings for each of the girls.
Step 1: Determine the common ratio.
Since we have two ratios involving three people, we need to find the common ratio to link all three ratios together. We can do this by setting up a proportion:
(Beatriz's savings)/(Hannah's savings) = (Hannah's savings)/(Julia's savings)
4/7 = 3/5
Cross-multiplying, we get:
4 * 5 = 7 * 3
20 = 21
This proportion is not valid, so let's find a new one.
Step 2: Find the common ratio.
Let's use the ratio between Beatriz's and Hannah's savings to find the common ratio between all three ratios:
(Beatriz's savings)/(Hannah's savings) = 4/7
To make the denominator of the fraction the same as the denominator in the second ratio, we can multiply both sides of the equation by 5:
(Beatriz's savings * 5) / (Hannah's savings * 5) = (4/7) * 5
20/35 = 20/35
This proportion is valid, so the common ratio is 5.
Step 3: Calculate the savings for each girl.
Let's use the total savings amount to calculate the actual savings for each girl.
Let X be the amount of money Beatriz has saved.
Since the ratio between Beatriz's and Hannah's savings is 4/7, Hannah's savings is (7/4) * X.
Since the ratio between Hannah's and Julia's savings is 3/5, Julia's savings is (5/3) * (7/4) * X.
The total savings is equal to the sum of each girl's savings:
X + (7/4) * X + (5/3) * (7/4) * X = $136
Simplifying the equation:
12X/12 + 21X/12 + 35X/12 = 136
Combining like terms:
68X/12 = 136
Multiply both sides by 12:
68X = 12 * 136
68X = 1632
Divide both sides by 68:
X = 24
So, Beatriz has saved $24, Hannah has saved (7/4) * 24 = $42, and Julia has saved (5/3) * (7/4) * 24 = $70.
Step 4: Calculate the difference in savings.
To find out 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 need to determine the individual savings for each girl.
Let's assume Beatriz's savings as 4x dollars. According to the given ratio, Hannah's savings would be 7x dollars.
Next, we need to determine Hannah's savings in relation to Julia's savings. The ratio states that Hannah's savings are in a ratio of 3:5 to Julia's savings. We can use this ratio to find the value of Hannah's savings relative to Julia's.
Let's assume that Hannah's savings are 3y dollars. According to the ratio, Julia's savings would be 5y dollars.
Now, we can set up an equation using the total savings amount given in the question.
Beatriz's savings (4x) + Hannah's savings (3y) + Julia's savings (5y) = $136
We can simplify this equation further:
4x + 3y + 5y = $136
Next, we need to find the values of x and y. One way to do this is to use trial and error. We can start with small values and incrementally increase them until the equation holds true.
By trying out different values, we find x = 4 and y = 8.
Plugging these values back into the equation, we get:
4(4) + 3(8) + 5(8) = $136
16 + 24 + 40 = $136
Now that we have determined the values for x and y, we can find the individual savings for each girl:
Beatriz's savings = 4x = 4(4) = $16
Hannah's savings = 3y = 3(8) = $24
Julia's savings = 5y = 5(8) = $40
Finally, to find out how much more money Julia has saved than Beatriz, we subtract Beatriz's savings from Julia's savings:
Julia's savings - Beatriz's savings = $40 - $16 = $24
Therefore, Julia has saved $24 more than Beatriz.