1.Six pears and three apples cost $3.90. Two pears and five apples cost $3.30. How much does one pear cost?
Hint: You have two unknowns (variables), so you need two equations. Write one equation for each situation and solve the system of equations.
6P + 3A=3.90
2P + 5A=3.30
Solve. I will be happy to critique your work.
HERE IS WHAT I GOT:A=.90
No, that is not right. Where is your work?
Printing a newsletter costs $.75 per copy plus $250 in printer's fees. The copies are sold for $2 each. How many copies of the newsletter must be sold to break even?
To solve this problem using a system of equations, let's represent the cost of one pear as P and the cost of one apple as A. We can set up the following system of equations based on the given information:
Equation 1: 6P + 3A = 3.90
Equation 2: 2P + 5A = 3.30
To solve this system, we can use the method of substitution or elimination. Let's use substitution:
From Equation 1, solve for P:
6P = 3.90 - 3A
P = (3.90 - 3A) / 6
Now substitute this expression for P into Equation 2:
2((3.90 - 3A) / 6) + 5A = 3.30
Let's simplify this equation:
(7.80 - 6A) / 6 + 5A = 3.30
Multiply both sides by 6 to eliminate the denominator:
7.80 - 6A + 30A = 19.80
Combine like terms:
24A = 12
Divide both sides by 24:
A = 0.50
Now substitute this value of A back into Equation 1 to find P:
6P + 3(0.50) = 3.90
6P + 1.50 = 3.90
6P = 3.90 - 1.50
6P = 2.40
P = 2.40 / 6
P = 0.40
Therefore, the cost of one pear is $0.40.