Question 310000: I hope this is right section. Please can you help me with this?
1. Ben has four times more money than Alfred. Penelope has one half the amount of money as Ben has. The total amount of money that Ben,
Alfred and Penelope have is R140.00.
Show by calculation the amount of money that each of them has.
3.2 Tom and Dick have a certain amount of money. The sum of four times the amount of money that Tom has and three times the amount of money that Dick has is R59.00. The difference between the amount of money that Tom an Dick have is R6,00. Using this information, show the calculation the amount of money that each Tom and Dick have.
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! 1. Let B = the amount that Ben has, A = the amount that Alfred has, and P = the amount hat Penelope has.
1) B = 4A "Ben has 4 times more money than Alfred."
2) P = (1/2)B "Penelope has one half the amount of money that Ben has."
3) A+B+P = R140.00 "The total amount that Ben, Alfred, and Penelope have is R140.00"
So you have three equations with three unknowns (B, A, & P).
By a process of elimination, you need to eliminate two of the variables so that you can find the value of one of them, then, by substitution, you can find the values of the other two.
Substitute equation 1) for B in equation 3) thus:
3a) A+4A+P = R140.00
Next, substitute equation 1) for B in eqation 2) thus:
2a) P = (1/2)(4A) = 2A and substitute this into equation 3a) to get:
3b) A+4A+2A = R140.00 Now solve for A.
7A = R140.00 and...
A = R20.00 Now you can find the values of B and P.
B = 4A
B = 4(20)
B = R80.00 and...
P = (1/2)B
P = (1/2)(80)
P = R40.00
Alfred has R20.00
Ben has R80.00
Penelope has R40.00
------------------
2.Let T = Tom's amount and D = Dick's amount.
1) 4T+3D = R59.00 "The sum of 4 times Tom's money and 3 times Dick's money is R59.00"
2) T-D = R6.00 "The difference between the amount that Tom and Dick have is R6.00"
Rewrite equation 2) as: T = D+R6.00 and substitute into equation 1).
1a) 4(D+6)+3D = 59 Simplify and solve for D.
4D+24+3D = 59
7D+24 = 59
7D = 35
D = R5.00 and...
T = D+6
T =5+6
T = R11.00
Tom has R11.00 and Dick has R5.00
|
|
|
