Question
Krista was assigned a homework problem that stated there were 45 stamps purchased for $18.75. Some stamps were 40 cents, and some stamps were 55 cents. To solve this problem, she wrote the system of equations that is shown below.
0.40 x + y = 45. x + 0.55 y = 18.75.
Which explains the error that Krista made?
Krista put 0.40 in the first equation meant for the number of stamps.
Krista put 0.55 in the second equation meant for the value of stamps.
Krista did not use the correct decimal to represent the total cost of the stamps.
Krista mistakenly put 45 in the first equation when it should have been in the second equation.
0.40 x + y = 45. x + 0.55 y = 18.75.
Which explains the error that Krista made?
Krista put 0.40 in the first equation meant for the number of stamps.
Krista put 0.55 in the second equation meant for the value of stamps.
Krista did not use the correct decimal to represent the total cost of the stamps.
Krista mistakenly put 45 in the first equation when it should have been in the second equation.
Answers
GPT-4o mini
Let's analyze Krista's system of equations to determine her mistake.
1. The problem states there are 45 stamps in total, which should be represented by the equation for the total number of stamps. This means if we let \( x \) be the number of 40-cent stamps and \( y \) be the number of 55-cent stamps, we should have:
\[
x + y = 45
\]
2. The total cost of the stamps, which is given as $18.75, can be represented by:
\[
0.40x + 0.55y = 18.75
\]
In Krista's equations:
- The first equation is \( 0.40x + y = 45 \), which is incorrect because it mixes the cost of stamps (0.40) with the total number of stamps (45).
- The second equation, \( x + 0.55y = 18.75 \), incorrectly places the number of stamps with the price.
Checking the options given:
- **"Krista put 0.40 in the first equation meant for the number of stamps."**: True, this is an error.
- **"Krista put 0.55 in the second equation meant for the value of stamps."**: Misleading, the structure of the equation is wrong.
- **"Krista did not use the correct decimal to represent the total cost of the stamps."**: Not applicable since the cost is represented correctly.
- **"Krista mistakenly put 45 in the first equation when it should have been in the second equation."**: Correct, she should have represented the total number of stamps in an equation rather than introducing a cost value.
From the analysis, the most accurate explanation of Krista's mistake is:
**"Krista put 0.40 in the first equation meant for the number of stamps."**
Explaining that she incorrectly utilized the stamp value in the total count equation.
1. The problem states there are 45 stamps in total, which should be represented by the equation for the total number of stamps. This means if we let \( x \) be the number of 40-cent stamps and \( y \) be the number of 55-cent stamps, we should have:
\[
x + y = 45
\]
2. The total cost of the stamps, which is given as $18.75, can be represented by:
\[
0.40x + 0.55y = 18.75
\]
In Krista's equations:
- The first equation is \( 0.40x + y = 45 \), which is incorrect because it mixes the cost of stamps (0.40) with the total number of stamps (45).
- The second equation, \( x + 0.55y = 18.75 \), incorrectly places the number of stamps with the price.
Checking the options given:
- **"Krista put 0.40 in the first equation meant for the number of stamps."**: True, this is an error.
- **"Krista put 0.55 in the second equation meant for the value of stamps."**: Misleading, the structure of the equation is wrong.
- **"Krista did not use the correct decimal to represent the total cost of the stamps."**: Not applicable since the cost is represented correctly.
- **"Krista mistakenly put 45 in the first equation when it should have been in the second equation."**: Correct, she should have represented the total number of stamps in an equation rather than introducing a cost value.
From the analysis, the most accurate explanation of Krista's mistake is:
**"Krista put 0.40 in the first equation meant for the number of stamps."**
Explaining that she incorrectly utilized the stamp value in the total count equation.