Maria has $50 to spend on buying apples and bananas. Apples cost $2 each and bananas cost $1.50 each. she wants to buy a total of 30 fruits the system and the graph represent the situation.
2x + 1.5y = 50.
x + y = 30
A. Are you can buy 20 apples and 10 bananas.
B. Maria can buy 15 apples and 15 bananas.
C. Maria can buy 25 apples and five bananas.
D. Maria can buy 18 apples and 12 bananas.
To solve the system of equations, we can use the substitution method.
From the second equation, we can rewrite it as x = 30 - y.
Substituting x = 30 - y into the first equation, we have:
2(30 - y) + 1.5y = 50
60 - 2y + 1.5y = 50
-0.5y = -10
y = 20.
Substituting y = 20 into x = 30 - y, we have:
x = 30 - 20
x = 10.
So Maria can buy 10 apples and 20 bananas.
Therefore, the correct answer is:
A. Maria can buy 20 apples and 10 bananas.
You sure?
Apologies for the mistake in my previous response. Let's solve the system of equations correctly.
The given system of equations is:
2x + 1.5y = 50 (equation 1)
x + y = 30 (equation 2)
To make the solution easier, let's multiply equation 2 by -2:
-2(x + y) = -2(30)
-2x - 2y = -60 (equation 3)
Now, add equation 1 and equation 3 together:
(2x + 1.5y) + (-2x - 2y) = 50 - 60
2x - 2x + 1.5y - 2y = -10
-0.5y = -10
y = (-10)/(-0.5)
y = 20
Substituting y = 20 into equation 2, we get:
x + 20 = 30
x = 10
Hence, the solution is x = 10 and y = 20.
Maria will be able to buy 10 apples and 20 bananas.
Therefore, the correct answer is A. Maria can buy 20 apples and 10 bananas.