SOLUTION: 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. Wri

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 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. Wri      Log On


   

Question 57309This question is from textbook
: 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.
Let p = the cost of one pear
Let a = the cost of one apple
a. Write a system of equations that can be used to determine the cost of pears and apples.
Determine the cost of one pear and one apple. Use mathematics to explain how you determined your answer.
This question is from textbook

Found 2 solutions by hayek, funmath:
Answer by hayek(51) About Me  (Show Source):
You can put this solution on YOUR website!
We'll use P to be the price of one pear and A to be the price of one apple:
First Equation: 6*P + 3*A = 3.90
Second Equation 2*P + 5*A = 3.30
Solve first eq. for P:
6P=3.90-3A
P=3.90/6 - 3A/6
Plug into second equation:
2*(3.90/6 - 3A/6) +5A = 3.30
Simplify:
1.3 - 6A/6 + 5A = 3.30
1.3 -A + 5A = 3.30
1.3 + 4A = 3.30
4A = 3.30-1.30
4A = 2
A = 0.5
So each apple (A) is $0.50
Plug into Eq 1 to find P: 6*P + 3*(.5)=3.90
6P + 1.5 = 3.90
6P =3.90-1.5
6P = 2.4
P = $.40
Solved by pluggable solver: Linear System solver (using determinant)
Solve:
+system%28+%0D%0A++++6%5Cp+%2B+3%5Ca+=+3.9%2C%0D%0A++++2%5Cp+%2B+5%5Ca+=+3.3+%29%0D%0A++

Any system of equations:


has solution

or



(p=0.4, a=0.5}

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
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.
Let p = the cost of one pear
Let a = the cost of one apple
a. Write a system of equations that can be used to determine the cost of pears and apples.
Determine the cost of one pear and one apple. Use mathematics to explain how you determined your answer.
:Six pears and three apples cost $3.90
Is the equation: 6p+3a=3.90
:Two pears and five apples cost $3.30
Is the equation: 2p+5a=3.30
:
Your system of two equations and two unknowns is:
6p+3a=3.90
2p+5a=3.30
:
Multiply the second equation by -3 and add it to the first equation to eliminate the p's and solve for a:
-3(2p+5a=3.30)---> -6p-15a=-9.90
:
6p+3a=3.90
-6p-15a=-9.90
_____________
-12a=-6.00
-12a/-12=-6.00/-12
a=$.50
Substitute a=.50 into one of the original equations and solve for p.
2p+5(.50)=3.30
2p+2.50=3.30
2p+2.50-2.50=3.30-2.50
2p=.8
2p/2=.8/2
p=$.40
The pears are $.40 a piece and the apples are $.50 a piece.
Happy Caclulating!!!!