SOLUTION: Can someone help me with this? 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),

Question 101072: Can someone help me with this?
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.
b. Determine the cost of one pear and one apple. Use mathematics to explain how you determined your answer

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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.
6p + 3a = 3.90
2p + 5a = 3.30
-----------------
Multiply the 2nd equation by 3 to get:
6p + 15a = 9.90
--------------
Subtract the 1st from this last to get:
12a = 6
a = 0.50 (cost of one apple)
---------------
Substitute that into 6p + 3a = 3.90
6p + 3*0.5 = 3.90
6p + 1.5 = 3.90
6p = 2.40
p = 0.60 (price of one pear)
==========================
Cheers,
Stan H.
b. Determine the cost of one pear and one apple.
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