joe had four times as many dimes as pennies in her pocket. she spent two dimes and got two pennies in change. Now she has three times as many dimes as pennies. jo started with how many dimes?
d=4P
(d-2)=3(P+2)
that should do it, two equations, two unknowns. Put them in standard form..
d-4P=0
d-3P=8
solve for d, P
To find out how many dimes Joe started with, we can solve the problem step by step.
Let's denote the number of pennies Joe started with as "P" and the number of dimes as "D." According to the information given in the problem:
1. Joe had four times as many dimes as pennies:
D = 4P
2. Joe spent two dimes and got two pennies in change. This means:
Joe had (D - 2) dimes left and (P + 2) pennies left.
3. Joe now has three times as many dimes as pennies:
D - 2 = 3(P + 2)
Now we can solve the system of equations by substituting the value of D from the first equation into the third equation:
4P - 2 = 3(P + 2)
Expanding the equation:
4P - 2 = 3P + 6
Subtracting 3P from both sides:
P - 2 = 6
Adding 2 to both sides:
P = 8
Now we know that Joe started with 8 pennies. To find the number of dimes, we substitute the value of P into the first equation:
D = 4P = 4(8) = 32
Therefore, Joe started with 32 dimes.