At the local grocery store, 6 bananas and 3 oranges cost $10. Also, 3 bananas and 5 oranges cost $12. What is the combined cost of one banana and one orange at the local grocery store? Round to the nearest cent.
6b+3o = 10
3b+5o = 12
12b+6o = 20
9b+15o = 36
21b+21o = 56
b+o = 56/21 = 2.67
To find the combined cost of one banana and one orange at the local grocery store, we can set up a system of equations.
Let's assign variables to the cost of one banana and one orange. Let's say the cost of one banana is x, and the cost of one orange is y.
From the information given, we can create the following equations:
Equation 1: 6x + 3y = 10
This equation represents the cost of 6 bananas and 3 oranges, which is $10.
Equation 2: 3x + 5y = 12
This equation represents the cost of 3 bananas and 5 oranges, which is $12.
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the method of substitution. We can rearrange Equation 1 to solve for x:
6x = 10 - 3y
x = (10 - 3y)/6
Now we substitute this expression for x into Equation 2:
3((10 - 3y)/6) + 5y = 12
Now we can simplify and solve for y:
(30 - 9y)/6 + 5y = 12
(30 - 9y + 30y)/6 = 12
30 - 9y + 30y = 72
-30y + 30 = 72
21y = 42
y = 42/21
y = 2
Now that we have found y, we can substitute it back into Equation 1 to find x:
6x + 3(2) = 10
6x + 6 = 10
6x = 4
x = 4/6
x = 2/3
So, the cost of one banana is approximately $0.67 (rounded to the nearest cent), and the cost of one orange is $2.
To find the combined cost of one banana and one orange, we simply add their individual costs:
Cost of one banana + Cost of one orange = $0.67 + $2 = $2.67
Therefore, the combined cost of one banana and one orange at the local grocery store is approximately $2.67 (rounded to the nearest cent).