Respuesta :
Answer: 60 quarters and 40 dimes
Step-by-step explanation:
Step 1: Setup Coin Value and Coin Total Equation:
Coin Value Equation → 0.1d + 0.25q = $19.00 where d = dimes and q = quarters
Coin Total Equation → d + q = 100
Step 2: Rearrange Coin Total Equation in terms of dimes (d)
d = 100 - q ← Revised Coin Total Equation
Step 3: Plug in our Revised Coin Total Equation for d into our Coin Value Equation:
0.1(100 - q) + 0.25q = $19.00
0.1(100) - 0.1(q) + 0.25q = $19.00
10 - 0.1q + 0.25q = $19.00
10 + (0.25 - 0.1)q = $19.00
10 + 0.15q = $19.00
Step 4: Subtract 10 from each side of the equation to isolate q
10 - 10 + 0.15q = $19.00 - 10
0.15q = 9
Step 5: Divide each side of the equation by 0.15 to isolate q
0.15q/0.15 = 9/0.15
q = 60
Step 6: Using our value for q, Solve for d using our Coin Total Equation:
d + 60 = 100
Subtracting 60 from both sides, we get d + 60 - 60 = 100 - 60
d = 40
Summarizing our word problem, we see that 60 quarters and 40 dimes add up to $19.00
