Frank has $20 less than Tracy. John has twice as much as Frank. Patty has three times as much as John. Together they have $340. How much does each person have?
I tried multiple different numbers but they were either more or less then $340
rather than guessing, do the math
f = t-20
j = 3f = 3(t-20) = 3t-60
p = 3j = 3(3t-60) = 9t-180
f+t+j+p = 340
Now you can solve the equations, knowing that the sum will be 340.
f+t+j+p =
t-20 + t + 3t-60 + 9t-180 = 340
14t-260 = 340
14t = 600
t = 300/7
Hmmm. I get a fraction, rather than an integer. Check for a typo.
Yea sir I did. That's the exact question. Maybe they wrote the question wrong
That does sometimes happen. If they had $440 in total, then you'd have
14t = 700
t = 50
That seems most likely.
To solve this problem, let's break it down step by step:
Step 1: Assign variables to represent the unknown amounts.
Let's represent the amount of money Tracy has as T.
Frank would have $20 less than Tracy, so we can represent the amount Frank has as F = T - $20.
John has twice as much money as Frank, so John's amount can be represented as J = 2F = 2(T - $20).
Patty has three times as much money as John, so Patty's amount can be represented as P = 3J = 3(2(T - $20)).
Step 2: Write an equation to represent the total amount of money they have.
Together they have $340, so the equation can be written as:
T + F + J + P = $340.
Step 3: Substitute the variables.
Using the variables we assigned, let's substitute them into the equation:
T + (T - $20) + 2(T - $20) + 3(2(T - $20)) = $340.
Step 4: Solve the equation.
Now, simplify the equation and solve for T:
T + T - $20 + 2T - $40 + 6(T - $20) = $340.
10T - $200 = $340.
10T = $340 + $200.
10T = $540.
T = $540 / 10.
T = $54.
Step 5: Find the amounts for the other individuals.
Now that we know Tracy has $54, we can find the amounts for the other people as well.
Frank's amount, F = T - $20, F = $54 - $20, F = $34.
John's amount, J = 2F, J = 2($34), J = $68.
Patty's amount, P = 3J, P = 3($68), P = $204.
Therefore, Tracy has $54, Frank has $34, John has $68, and Patty has $204. Together they add up to $340.