Jocelyn has $1.95 in her pocket made up of 27 coins: a combination of nickels and dimes. How many of each type of coin does she have?
Answer (2)
Define n as the number of nickels and d as the number of dimes.
Set up the equations: n + d = 27 and 5 n + 10 d = 195 .
Solve for d using substitution: d = 12 .
Solve for n : n = 15 . The final answer is 15 nickels and 12 dimes .
Explanation
Problem Analysis Let's analyze the problem. We know that Jocelyn has a total of 27 coins, which are a combination of nickels and dimes. The total value of these coins is $1.95. Our goal is to find out how many nickels and how many dimes she has.
Setting up Equations Let's use variables to represent the unknowns. Let n be the number of nickels and d be the number of dimes. We can set up two equations based on the given information. The first equation represents the total number of coins: n + d = 27 The second equation represents the total value of the coins in cents (since 1.95 i se q u a lt o 195 ce n t s ) : 5 n + 10 d = 195 $
Expressing n in terms of d Now we need to solve this system of equations. We can use the substitution or elimination method. Let's use the substitution method. From the first equation, we can express n in terms of d :
n = 27 − d
Substitution Substitute this expression for n into the second equation: 5 ( 27 − d ) + 10 d = 195
Solving for d Now, let's simplify and solve for d :
135 − 5 d + 10 d = 195 5 d = 195 − 135 5 d = 60 d = 5 60 d = 12
Solving for n Now that we have the value of d , we can find the value of n :
n = 27 − d n = 27 − 12 n = 15
Final Answer So, Jocelyn has 15 nickels and 12 dimes.
Examples
Imagine you are a cashier and need to quickly count the number of nickels and dimes in a customer's handful of change to ensure you have enough of each for making change. By setting up a system of equations similar to the one we solved, you can efficiently determine the exact number of each coin type, helping you manage your cash drawer effectively and provide better service.
Jocelyn has 15 nickels and 12 dimes. This was determined by setting up equations based on the total number of coins and their total value. Solving these equations allowed us to find the number of each type of coin she has.
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