Ali, Clara, and Shan raised money for new books for the school library. Ali raised 20% more than Clara and $58 more than Shan. Clara raised 1/4 more than Shan.
A) How much money did they raise altogether
B) What percent of the total money did Clara raise?
Thank you, btw five stars if you help. :)
To solve this problem, we need to break it down step by step:
Step 1: Assign variables
Let's assign the variables:
- Ali's amount raised as A
- Clara's amount raised as C
- Shan's amount raised as S
Step 2: Translate the given information into equations
From the given information, we can write down the following equations:
1) Ali raised 20% more than Clara: A = C + 0.2C
2) Ali raised $58 more than Shan: A = S + $58
3) Clara raised 1/4 more than Shan: C = S + (1/4)S = S + 0.25S
Step 3: Solve the equations
Now we can solve the equations to find the values of A, C, and S. Let's solve them one by one:
From equation 2, we can substitute A with S + $58:
S + $58 = C + 0.2C
Simplifying equation 2:
1.2C = S + $58
Now let's substitute C with S + 0.25S in equation 1:
A = C + 0.2C
A = (S+0.25S) + 0.2*(S+0.25S)
A = 1.45S + 0.45S
Substituting A with S + $58 in the above equation:
1.45S + 0.45S = S + $58
Simplifying the equation:
1.9S = $58
Solving for S:
S = $58 / 1.9
Within Step 3, we have found the value of S. To find A and C, we'll substitute the value of S back into equations 2 and 3.
Step 4: Calculate the values
Using the value of S, we can calculate the values of A and C:
From equation 2:
A = S + $58
A = ($58 / 1.9) + $58
From equation 3:
C = S + 0.25S
C = ($58 / 1.9) + 0.25 * ($58 / 1.9)
Step 5: Calculate the total amount raised
To find the total amount raised (T), we add the individual amounts together:
T = A + C + S
Step 6: Calculate the percentage Clara raised
To find the percentage Clara raised, we divide Clara's amount raised (C) by the total amount raised (T) and multiply by 100:
Percentage Clara raised = (C / T) * 100
Now, you can substitute the values of A, C, and S into steps 5 and 6 to find the final answers.
I hope this explanation helps! Let me know if you have any further questions.
clara raised x
ali raised 1.2 x
shan raised 1.2 x - 58
x = 5/4 (1.2 x - 58)
4 x = 6 x - 290
2 x = 290
x = 145
now you do the rest
a) $435
b) 33.33%
145 + 2.4*145 -58 = 435
145/435 = .3333