if there are 45 pieces of fruit and there are twice as many bananas as there are apples. How many of each kind of fruit are there?
a = apples
b = bananas = 2a
a + 2 a = 45
3 a = 45
a = 15
b = 2 a = 30
x + 2x = 45
3x = 45
x = 15
15 apples
30 bananas
To solve this problem, let's start by assigning variables to represent the unknown quantities. Let's say "A" represents the number of apples, and "B" represents the number of bananas.
We know that there are 45 pieces of fruit, so we can form the equation:
A + B = 45
We also know that there are twice as many bananas as apples, which gives us the equation:
B = 2A
Now we can solve the system of equations:
Substitute the value of B from the second equation into the first equation:
A + 2A = 45
Combine like terms:
3A = 45
Divide by 3:
A = 15
Now substitute the value of A into the second equation to find the value of B:
B = 2(15)
B = 30
So, there are 15 apples and 30 bananas.