three apples and four bananas cost $4.85,three apples and ten bananas cost $8.75, find the cost of an apple
Let A be the Apple cost and B be the banana cost.
3A + 4B = $4.85
3A + 10B = $8.75
Subtract the first equation from the second.
6B = 3.90
B = 0.65
3A + 4B = 3A + 2.60 = 4.85
3A = 2.25
A = 0.75
berts age is 30. three times berts age plus 8 times ernie age is 108 how old are bert and ernie
four pounds of apples cost $1.96
To find the cost of an apple, we can set up a system of equations based on the given information. Let's define the cost of an apple as 'a' and the cost of a banana as 'b'.
From the first statement, "three apples and four bananas cost $4.85", we can write the equation:
3a + 4b = 4.85 (Equation 1)
From the second statement, "three apples and ten bananas cost $8.75", we can write the equation:
3a + 10b = 8.75 (Equation 2)
Now, we have a system of two equations that can be solved simultaneously to find the values of 'a' and 'b'. Here's how we can do that:
Step 1: Multiply Equation 1 by 5 and Equation 2 by 3 to eliminate 'a' when we add the equations together:
15a + 20b = 24.25 (Equation 3)
9a + 30b = 26.25 (Equation 4)
Step 2: Subtract Equation 3 from Equation 4 to eliminate 'a':
(9a + 30b) - (15a + 20b) = 26.25 - 24.25
-6a + 10b = 2 (Equation 5)
Step 3: Solve Equation 5 for 'a' by isolating it:
-6a = 2 - 10b
a = (10b - 2) / -6
a = (2 - 10b) / 6 (Equation 6)
Now that we have the expression for 'a' in terms of 'b', we can substitute this into one of the original equations to solve for 'b'. Let's use Equation 2:
3a + 10b = 8.75
Substituting Equation 6 into this equation:
3[(2 - 10b) / 6] + 10b = 8.75
Simplifying:
(6 - 30b) / 6 + 10b = 8.75
6 - 30b + 60b = 52.50
30b = 46.50
b = 46.50 / 30
b = 1.55
Now, substituting this value of 'b' back into Equation 6 to find 'a':
a = (2 - 10b) / 6
a = (2 - 10(1.55)) / 6
a = (2 - 15.5) / 6
a = -13.5 / 6
a = -2.25
However, it doesn't make sense for the cost of an apple to be negative. So, there must have been an error in the calculations. Let's review the equations and try solving it again.