Amy went to the fall festival and bought at least 25 apples. The apples were a mix of gala apples and red delicious apples. Amy knows that she got more than twice as many gala apples as she did red delicious apples. This can be represented by the system below:
x + y > 25
x > 2y
where x is the number of gala apples and y is the number of red delicious apples.
Which of the following is true?
Select one:
a. Amy could have purchased 20 gala apples and 10 red delicious apples.
b. All of these are possible.
c. Amy could have purchased 25 gala apples and 10 red delicious apples.
d. Amy could have purchased 5 gala and 25 red delicious apples.
she got MORE THAN twice as many gala
a. wont be more than.
b. already eliminated
c. Is 25 MORE THAN twice ten?
d. silly answer.
To determine which option is true, we need to satisfy both conditions given in the system of equations:
1. x + y > 25 (Amy bought at least 25 apples)
2. x > 2y (Amy bought more than twice as many gala apples as red delicious apples)
Let's evaluate each option:
a. Amy could have purchased 20 gala apples and 10 red delicious apples.
In this case, x = 20 and y = 10.
Condition 1: x + y = 20 + 10 = 30, which is greater than 25. So, this condition is satisfied.
Condition 2: x = 20 and y = 10. Since 20 is not greater than 2 times 10, this condition is not satisfied.
Therefore, option a is not true.
b. All of these are possible.
Since we have already determined that option a is not true, we can conclude that option b is also not true.
c. Amy could have purchased 25 gala apples and 10 red delicious apples.
In this case, x = 25 and y = 10.
Condition 1: x + y = 25 + 10 = 35, which is greater than 25. So, this condition is satisfied.
Condition 2: x = 25 and y = 10. Since 25 is greater than 2 times 10, this condition is satisfied.
Therefore, option c is true.
d. Amy could have purchased 5 gala and 25 red delicious apples.
In this case, x = 5 and y = 25.
Condition 1: x + y = 5 + 25 = 30, which is greater than 25. So, this condition is satisfied.
Condition 2: x = 5 and y = 25. Since 5 is not greater than 2 times 25, this condition is not satisfied.
Therefore, option d is not true.
In conclusion, the only true option is c. Amy could have purchased 25 gala apples and 10 red delicious apples.