Violet has $1.60 worth of nickels and dimes. She has a total of 21 nickels and dimes altogether. Determine the number of nickels and the number of dimes that Violet has.
Question
Violet has $1.60 worth of nickels and dimes. She has a total of 21 nickels and dimes altogether. Determine the number of nickels and the number of dimes that Violet has.
Solution
Step 1: Let's assume the number of nickels Violet has is represented by 'n' and the number of dimes she has is represented by 'd'.
Step 2: We know that the total value of nickels and dimes Violet has is 0.05 and each dime is worth $0.10, we can write the equation:
0.05n + 0.10d = 1.60
Step 3: We also know that the total number of nickels and dimes Violet has is 21. So we can write another equation:
n + d = 21
Step 4: Now we have a system of two equations with two variables. We can solve this system to find the values of 'n' and 'd'.
Step 5: Let's solve the second equation for 'n':
n = 21 - d
Step 6: Substitute this value of 'n' into the first equation:
0.05(21 - d) + 0.10d = 1.60
Step 7: Simplify the equation:
1.05 - 0.05d + 0.10d = 1.60
Step 8: Combine like terms:
0.05d = 0.55
Step 9: Divide both sides of the equation by 0.05:
d = 11
Step 10: Substitute this value of 'd' back into the second equation to find 'n':
n + 11 = 21
Step 11: Subtract 11 from both sides of the equation:
n = 10
Step 12: Therefore, Violet has 10 nickels and 11 dimes.
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