Ryan bought 6 apples and 9 peaches for a total of $9.75. Madi bought 4 apples and 5 peaches for $5.75.
How much are apples and peaches?
You can use two equations in 2 unknowns to solve. Let A be the apples and B be the peaches.
6A + 9B = 9.75
4A + 5B = 5.75
If you use the process of "elimination" that is multiply all part of the first equation by -4 and all parts of the second equation by 6 then add them up you will solve for the cost of a peach.
Does this ring any bells as a hint?
Do u have the answers for all of Ms. Stevens' class assignments?
To find the price of apples and peaches, we can set up a system of equations.
Let's assume the cost of an apple is "A" and the cost of a peach is "P".
From the information given, we can create the following equations:
Equation 1: 6A + 9P = 9.75
Equation 2: 4A + 5P = 5.75
Now we can solve this system of equations.
Multiplying both sides of Equation 2 by 2, we get:
8A + 10P = 11.50
Now let's subtract Equation 1 from this new equation:
8A + 10P - (6A + 9P) = 11.50 - 9.75
Simplifying, we get:
2A + P = 1.75
Now we have a new equation linking the variables A and P. We can isolate one of the variables by substituting this equation into one of the original equations. Let's use Equation 1:
6A + 9P = 9.75
Substituting the value of (2A + P) from the other equation, we get:
6A + 9(2A + P) = 9.75
Expanding and simplifying, we get:
6A + 18A + 9P = 9.75
Combining like terms, we get:
24A + 9P = 9.75
Now we can substitute the value of (2A + P) from the other equation:
24A + 9(1.75) = 9.75
Simplifying, we get:
24A + 15.75 = 9.75
Subtracting 15.75 from both sides, we get:
24A = 9.75 - 15.75
Simplifying, we get:
24A = -6
Dividing both sides by 24, we get:
A = -0.25
Now we can substitute the value of A into one of the original equations, let's use Equation 1:
6(-0.25) + 9P = 9.75
Simplifying, we get:
-1.5 + 9P = 9.75
Adding 1.5 to both sides, we get:
9P = 11.25
Dividing both sides by 9, we get:
P = 1.25
Therefore, the cost of an apple is $0.25 (or 25 cents) and the cost of a peach is $1.25 (or 1 dollar and 25 cents).