Serene had 4/7 as many as many chocolates as Melvin. Melvin had 4/5 as many chocolates as Esther. If Esther had 38 more chocolates than Serene, find the total number of chocolates that was shared among these 3 children at first
s = 4/7 m
m = 4/5 e
e = 38+s
solve for s,m,e and you find that
32+56+70 = 158
let the number of Esther’s be x
Melvin: 4/5x
Serene: 4/7 * 4/5x = 16/35x
x - 16/35x = 38
19/35x = 38
x = 38 * 35/19
x = 70
the total number = 70 + 4/5 * 70 + 16/35 * 70
= 70 + 56 + 32
= 158
To solve this problem, let's break it down step by step:
Step 1: Set up equations
Let's assign variables to the unknowns:
- Let's say the number of chocolates Serene had is S.
- The number of chocolates Melvin had is M.
- The number of chocolates Esther had is E.
From the given information, we can set up the following equations:
1) S = (4/7)M -- Serene had 4/7 as many chocolates as Melvin.
2) M = (4/5)E -- Melvin had 4/5 as many chocolates as Esther.
3) E = S + 38 -- Esther had 38 more chocolates than Serene.
Step 2: Solve the equations
We can start by substituting equation (2) into equation (1) to eliminate M. Rewrite equation (1) as:
S = (4/7)((4/5)E)
Simplifying this equation:
S = (16/35)E
Now, substitute equation (3) into equation (1) to eliminate S. Rewrite equation (1) as:
(S + 38) = (4/7)M
Simplifying this equation:
M = (7/4)(S + 38)
Now, substitute equation (2) into equation (3) to eliminate E. Rewrite equation (3) as:
E = (5/4)M
Simplifying this equation:
E = (5/4)[(7/4)(S + 38)]
Step 3: Find the total number of chocolates
To find the total number of chocolates shared among these 3 children, we need to evaluate the sum of S, M, and E.
Substituting the simplified equations back into equation (3), we have:
(5/4)[(7/4)(S + 38)] = S + 38
Now, solve this equation for S.
After finding the value of S, substitute it back into the other equations to find the values of M and E.
Finally, calculate the sum of S, M, and E, which will give you the total number of chocolates shared among these 3 children at first.