an orange has 20 fewer calories than a banana. If 7 bananas have the same number of calories as 9 oranges, how many calories are in a banana?
Let X be the number of calories in a banana, and Y be the number in an orange.
7X = 9Y
7X - 9Y = 0
X - Y = 20
9X - 9Y = 180
2X = 180
X = 90
Y = X -20 = 70
To solve this problem, we can use algebraic equations. Let's represent the number of calories in a banana as "B" and the number of calories in an orange as "O."
Given that an orange has 20 fewer calories than a banana, we can set up the equation:
O = B - 20 (Equation 1)
We also know that 7 bananas have the same number of calories as 9 oranges. So we can set up another equation:
7B = 9O (Equation 2)
Now we can substitute Equation 1 into Equation 2 to solve for B:
7B = 9(B - 20)
Multiply through the parentheses:
7B = 9B - 180
Subtract 9B from both sides to isolate the B term:
-2B = -180
Divide both sides by -2:
B = -180 / -2
B = 90
Therefore, there are 90 calories in a banana.