- A = 1, B = 10 (1 apple and 10 bananas)
- A = 5, B = 6 (5 apples and 6 bananas)
- A = 8, B = 3 (8 apples and 3 bananas)
Zendaya bought 6 apples and 5 bananas, which is the correct combination that satisfies both equations.
Let's denote the number of apples Zendaya bought as A and the number of bananas as B. We know that:
The total cost of apples and bananas is $6.
She bought a total of 11 apples and bananas.
We can write the equations as follows:
- 0.75A + 0.30B = 6 (Total cost equation)
- A + B = 11 (Total number equation)
First, we will determine three ways to have a total of 11 apples and bananas:
- A = 1, B = 10 (1 apple and 10 bananas)
- A = 5, B = 6 (5 apples and 6 bananas)
- A = 8, B = 3 (8 apples and 3 bananas)
Next, we will check which of these combinations satisfies the total cost equation:
- 0.75(1) + 0.30(10) = 0.75 + 3 = 3.75 (This doesn't equal 6, so it's not a solution)
- 0.75(5) + 0.30(6) = 3.75 + 1.80 = 5.55 (This doesn't equal 6, so it's not a solution)
- 0.75(8) + 0.30(3) = 6 + 0.90 = 6.90 (This doesn't equal 6, so it's not a solution)
None of these three combinations satisfy the total cost equation. Let's solve the system of equations to find the correct number of apples and bananas:
To solve this system, we can use the substitution or elimination method. We'll use the substitution method here. We can rewrite the second equation to isolate either A or B. We'll isolate A:
A = 11 - B
Now substitute this expression for A into the first equation:
0.75(11 - B) + 0.30B = 6
Expand the equation:
8.25 - 0.75B + 0.30B = 6
Combine like terms:
-0.45B = -2.25
Divide by -0.45:
B = 5
Now we can substitute this value of B back into the equation for A:
A = 11 - 5
A = 6