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In Mathematics / College | 2025-07-07

Giuliana has 22 quarters and dollar coins worth a total of $10.75. Which equation can be used to find $d$, the number of dollar coins Giuliana has?

A. $d-22+0.25 d=10.75$
B. $0.25 d+22-d=10.75$
C. $0.25(22-d)+d=10.75$
D. $d+0.25(d-22)=10.75$

Asked by xgnhrngfb7

Answer (1)

Define d as the number of dollar coins.
Express the number of quarters as 22 − d .
Write the equation representing the total value: d + 0.25 ( 22 − d ) = 10.75 .
The correct equation to find d is 0.25 ( 22 − d ) + d = 10.75 ​ .

Explanation

Problem Analysis Let's analyze the problem. Giuliana has a mix of quarters and dollar coins, totaling 22 coins. The total value of all the coins is $10.75 . We need to find an equation that we can use to determine the number of dollar coins, which we'll call d .

Finding the Number of Quarters Since Giuliana has 22 coins in total, and d of them are dollar coins, the remaining coins must be quarters. So, the number of quarters is 22 − d .

Calculating the Value of Each Type of Coin Now, let's think about the value of the coins. Each dollar coin is worth $1 , so the total value of the dollar coins is 1 × d = d dollars. Each quarter is worth $0.25 , so the total value of the quarters is 0.25 × ( 22 − d ) = 0.25 ( 22 − d ) dollars.

Forming the Equation The total value of all the coins is the sum of the value of the dollar coins and the value of the quarters. We know this total value is $10.75 . So, we can write the equation: d + 0.25 ( 22 − d ) = 10.75

Comparing with the Options Now, let's compare our equation to the options given:



d − 22 + 0.25 d = 10.75 (Incorrect)
0.25 d + 22 − d = 10.75 (Incorrect)
0.25 ( 22 − d ) + d = 10.75 (Correct)
d + 0.25 ( d − 22 ) = 10.75 (Incorrect)


Final Answer The correct equation is 0.25 ( 22 − d ) + d = 10.75 .

Examples
Imagine you're running a lemonade stand, and at the end of the day, you have a mix of nickels and dimes totaling 30 coins. Your total earnings are $$2.25. By setting up an equation similar to the one in this problem, you can figure out exactly how many nickels and dimes you have. This kind of problem-solving is useful in managing inventory, counting money, and making sure your accounts balance!

Answered by GinnyAnswer | 2025-07-07

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