Answer:
d = 27
Explanation:
We need a stem of equations to find d, the number of dimes.
First equation:
We know that the sum of the number of dimes and pennies (p) equals 3:
0.10d + 0.01p = 3
Second equation:
We also know that the number of pennies is 3 more than the number of dimes:
p = d + 3
Plug in p = d + 3 for p in 0.10d + 0.01p = 3 to find d:
0.10d + 0.01(d + 3) = 3
0.10d + 0.01d + 0.03 = 3
0.11d + 0.03 = 3
0.11d = 2.97
d = 27
Thus, Taylor has 27 dimes.
Optional step:
We can check our work by finding the number of pennies. We can do this by plugging in 27 for d in p = d + 3:
p = 27 + 3
p = 30
Now we can plug in 2 for d and 30 for p in p = d + 3 and 0.01p + 0.10d = 3. If we get the same answer on both sides of the equaitons for both equations, our answer for the number of dimes is correct:
Checking solutions with p = d + 3:
30 = 27 + 3
30 = 30
Checking solutions with 0.01p + 0.10d = 3:
0.01(30) + 0.10(27) + 3
0.30 + 2.70 = 3
3 = 3
Thus, our answers are correct.