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13 Feb 2024, 22:16
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D
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Derrick has a total of $13.75 in $0.25 coins and $1 bills. If Derrick has 5 more $0.25 coins than $1 bills, what is the sum of the number of $0.25 coins and the number of $1 bills that Derrick has?
A. 11
B. 15
C. 21
D. 25
E. 35
A. 11
B. 15
C. 21
D. 25
E. 35
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13 Feb 2024, 22:54
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DerekLin
The number of $1 bills that Derrick has = x
The number of $0.25 coins that Derrick has = x + 5
x + 0.25(x + 5) = 13.75
1.25x + 1.25 = 13.75
1.25x = 12.50
x = 10
Therefore,
- The number of $1 bills that Derrick has = x = 10
- The number of $0.25 coins that Derrick has = x + 5 = 15
The sum of the number of $0.25 coins and the number of $1 bills that Derrick has = 10 + 15 = 25
Option D
24 Aug 2024, 18:52
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Alternative Approach
Derrick has a total of $13.75 in $0.25 coins and $1 bills. If Derrick has 5 more $0.25 coins than $1 bills, what is the sum of the number of $0.25 coins and the number of $1 bills that Derrick has?
We know that Derrick has 5 more $0.25 coins than $1 bills. So, since the answer choices are relatively small numbers, we can simply check the answer choices to see which works.
When testing answer choices, it often works best to start with the middle value and then, depending on how that value works, decide whether we need to go up or down the values.
A. 11
B. 15
C. 21
D. 25
E. 35
So, we start with 21, which equals 5 + 16. So, with a total of 21, the number of $1 bills is 8 and the number of $0.25 coins is 8 + 5 = 13.
Without even calculating 0.25 × 13, we can see that 8 + (0.25 × 13) < 13.75 since 13.75 is almost 14 = 8 + 6 and there's no way 0.25 × 13 is close to 6. So, we need a greater total number of coins.
The only two choices greater than 21 are 25 and 35.
35 is clearly too high since 35 = 30 + 5, meaning we'd have 15 $1 bills, which is already greater than $13.75 without the $0.25 coins.
So, using this inelegant approach, we can pretty quickly determine that 25 is the correct answer.
Correct answer: D
Derrick has a total of $13.75 in $0.25 coins and $1 bills. If Derrick has 5 more $0.25 coins than $1 bills, what is the sum of the number of $0.25 coins and the number of $1 bills that Derrick has?
We know that Derrick has 5 more $0.25 coins than $1 bills. So, since the answer choices are relatively small numbers, we can simply check the answer choices to see which works.
When testing answer choices, it often works best to start with the middle value and then, depending on how that value works, decide whether we need to go up or down the values.
A. 11
B. 15
C. 21
D. 25
E. 35
So, we start with 21, which equals 5 + 16. So, with a total of 21, the number of $1 bills is 8 and the number of $0.25 coins is 8 + 5 = 13.
Without even calculating 0.25 × 13, we can see that 8 + (0.25 × 13) < 13.75 since 13.75 is almost 14 = 8 + 6 and there's no way 0.25 × 13 is close to 6. So, we need a greater total number of coins.
The only two choices greater than 21 are 25 and 35.
35 is clearly too high since 35 = 30 + 5, meaning we'd have 15 $1 bills, which is already greater than $13.75 without the $0.25 coins.
So, using this inelegant approach, we can pretty quickly determine that 25 is the correct answer.
Correct answer: D
