Edward has $40 more thanFariq. If Edward gives 1/5 of his money to Fariq. Fariq will have7/8 as much money as Edward. How much money do they have altogether.
i do not know if i uderstand the question but i'll try:
money Fariq call them x
Edward money x+40
If Edward gives 1/5 of his money to Fariq => Fariq as x+ 1/5 Edward money(x+40)/5,
Fariq as x+(x+40)/5
i did not understand if Fariq has 7/8 of the money that now Edward. if so =>
FariqMoney[x]+donationEdward[(x+40)/5]=7/8EdwardMoneynow[(x+40)-(x+40)/5]
eq: x+(x+40)/5=7/8[(x+40)-(x+40)/5]
...perhaps... x=74,Fariq 74, Ed 74+40
tot 74+74+40
let the current amounts be e,f
e = f+40
After e gives 1/5 of his money to f,
(f + 1/5 e) = 7/8 (4/5 e)
e = 80
f = 40
e+f = 120
check: after e gives f 1/5 of $80 = $16,
e has $64, f has $56, which is 7/8 of $64
To solve this problem, let's first assign variables to represent the amounts of money Edward and Fariq have.
Let's say Edward has E dollars, and Fariq has F dollars.
Given that Edward has $40 more than Fariq, we can write the equation:
E = F + $40 ------ (Equation 1)
Next, we are told that if Edward gives 1/5 of his money to Fariq, Fariq will have 7/8 as much money as Edward. We can express this as an equation as well.
After Edward gives away 1/5 of his money, he will have 4/5 of his initial amount remaining. So, Fariq will have 7/8 of 4/5 of Edward's initial amount, or (7/8) * (4/5) * E dollars.
Now, we can set up the second equation:
F + (7/8) * (4/5) * E = (7/8) * E ------ (Equation 2)
To find the values of E and F, we can solve this system of equations.
Let's start by simplifying Equation 2:
F + (7/10) * E = (7/8) * E
Next, let's get rid of the fractions by multiplying both sides of the equation by the least common multiple (LCM) of 10 and 8, which is 40:
40F + 28E = 35E
Now, let's simplify further:
40F + 28E - 35E = 0
40F - 7E = 0 ------ (Equation 3)
Now we have two equations:
E = F + 40 ------ (Equation 1)
40F - 7E = 0 ------ (Equation 3)
To solve this system of equations, we can use the substitution method.
From Equation 1, we can express F in terms of E:
F = E - 40
Substitute this value of F into Equation 3:
40(E - 40) - 7E = 0
Now simplify the equation:
40E - 1600 - 7E = 0
33E = 1600
E ≈ 48.48
Finally, substitute this value of E back into Equation 1 to find F:
F = 48.48 - 40
F ≈ 8.48
Hence, Edward has approximately $48.48, and Fariq has approximately $8.48.
To find the total amount of money they have together, add their amounts:
Total = E + F
Total ≈ $48.48 + $8.48
Total ≈ $56.96
Therefore, Edward and Fariq have approximately $56.96 altogether.