Hank has more money than Joe and Al combined. Joe has exactly twice as much money as Al. Al has more money than Steve. Hank has exactly four times as much money as Steve. None of the boys have more than 18tf. The total amount of money the fours boys have is ____ cents.
j = 2a
h > j+a , h > 3a or a < (1/3)h
h = 4s
a > s
assuming that all the monies are whole numbers
from h = 4s, we know h must be a multiple of 4,
h: 4, 8, 12, 16 , remember h ≤ 18
s: 1, 2, 3, 4
a < (1/3)h
a < 5
a = 1, 2, 3, 4
j = 2, 4, 6, 8
cases:
h s a j
12 3 1 2
12 3 2 4
12 3 3 6
12 3 4 8
none of these cases seem to fit our conditions
What is the meaning of 18tf ??
I just read it as 18 units of money
cents*
To find the total amount of money the four boys have, we need to analyze the given information step by step.
Let's assign variables to each boy's money:
- Let's say Al has x cents.
- Joe will have twice the amount as Al, so Joe has 2x cents.
- Steve has less money than Al, but we don't know the exact amount at this stage.
- Hank has four times the amount Steve has, so Hank has 4 * Steve's amount.
Now, let's break down the given information into equations:
1. Hank has more money than Joe and Al combined:
H > J + A
H > 2x + x
H > 3x
2. Joe has exactly twice as much money as Al:
J = 2A
J = 2x
3. Al has more money than Steve:
A > S
4. Hank has exactly four times as much money as Steve:
H = 4S
Since none of the boys have more than 18tf, we know that the maximum amount any boy can have is 18tf. In cents, 18tf is equal to 1800 cents.
Now, let's solve the system of equations:
We have two equations involving H, J, and A:
H > 3x and H = 4S
Since H must have the smallest possible value to satisfy both equations, let's assume H = 3x.
Substituting H = 3x into H = 4S, we get 3x = 4S, which implies that 3x is divisible by 4.
We can assume x = 4, which means Al has 4 cents. Then, Joe has 2x = 2 * 4 = 8 cents. Since Al has more money than Steve, let's assume S = 3, which means Steve has 3 cents. Finally, Hank has 4 * S = 4 * 3 = 12 cents.
The total amount of money the four boys have is A + J + S + H = 4 + 8 + 3 + 12 = 27 cents.