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.
Six pears and three apples cost $3.90. Two pears and five apples cost $3.30. How much does one pear cost?
6p + 3a = 3.90

2p + 5a = 3.30

Divide the first equation by 3:

2p + a = 1.30

Restate:

a = 1.30 - 2p

Substitute 1.30 - 2p for a in the second equation:

2p + 5(1.30-2p) = 3.30

2p + 6.50 - 10p = 3.30

-8p = -3.20

p = .40

Substitute .40 for p in either original equation:

6(.40) + 3a = 3.90

2.40 + 3a = 3.90

3a = 1.50

a = .50

One pear costs $0.40

One apple costs $0.50
Reply:a)

8p + 8a = 7.20 (that's the two costs added together.)

----------- -------

16 16 (to get rid of the multiples.)



p + a = .45

---------------

2 (to find the cost of one... assuming they cost the same.)



one apple costs .225 cents (about 23 cents.)



b) one pear costs about 23 cents. same with one apple. I determined the answer by combining the variables and end results. then I did the linear equation to find the values of each variable, assuming the cost of the pears and apples were the same.



hope i helped =]]
Reply:a. 6p+3a=3.90

2p+5a=3.30



b. First equation

take 6p from each side

3a=3.90-6p

divide by 3

a=1.30-2p



substitute a in the next equation

2p+5(1.30-2p)=3.30

simplify

2p+6.50-10p=3.30

-8p+6.50=3.30

-8p=-3.2

since both are negative they can both change

8p=3.20

divide by 8

p=.40



If p=.40 and a= 1.30-2p



a=1.30-.80

a=.50
Reply:6p + 3a = 3.90

2p + 5a = 3.30



multiply 2p + 5a = 3.30 by -3.....you get -6p - 15a = -9.90

combine the two equations (6p + 3a = 3.90) and (-6p - 15a = -9.90)....you get -12a = -6

solve for a

you get a = 0.50



substitute 0.50 into 2p + 5a = 3.30

2p + 5(0.50) = 3.30

2p + 2.5 =3.30

2p = 0.80

p = $0.40



I got 40 cents. Now finish you're homework kid.
Reply:A Six pears and three apples cost $3.90

B So, dividing by three, two pears and an apple cost $1.30

C But, two pears and five apples cost $3.30

D The difference between B and C is four apples and $2

E So an apple costs 50c

F So, from B, if two pears and a 50c apple costs $1.30, then two pears cost 80c

G So, a pear costs 40c





Who needs algebra to solve the equation?
Reply:Too much. You should wait until they are in season locally.
Reply:15 cents
Reply:omg, what grade r u in?



Oh and I have no idea.... hehe
Reply:Okay, here we go.



Your sytem of equations would be

6p + 3a = 3.90

2p + 5a = 3.30



6 because thats the number of pears in the first sentence.

3 because thats the number of apples in the first sentence.

2 because thats the number of pears in the second sentence.

5 because thats the number of apples in the second sentence.





(5)6p + 3a = 3.90

(-3)2p + 5a = 3.30



30p + 15a = 19.50

-6p -15a = - 9.90



times 5 to the first line and -3 to the second so that the amount of apples equal each other (on both lines) and they cancel each other out.



Now you're left with

30p = 19.50

-6p = -9.90



Subtract 6 from thirty and 9.90 from 19.50



24p = 960



Divited 960 by 24 and you get 40 %26lt;--- thats how much the pears cost (for one)



Next do the same for the apples (this time making the pears equal each other out to cancel themselves.)



6p + 3a = 3.90

(-3)2p + 5a = 3.30



times the bottom equation ONLY by -3



6p + 3a = 3.90

-6p - 15a = -9.90



Cancel out the p's (pears)



3a = 3.90

-15a = -9.90



Add together



-12a = -600



Divide -600 by -12



a = 50



Which means 1 pear costs 40 cents and 1 apple costs 50.





Check:

Replace the variables (p, a) with the answers (40 for pears, 50 for apples) and add them up.



6(40) + 3(50) = 3.90

2(40)+5(50) = 3.30



2.40 + 1.50 = 3.90

.80 + 2.50 = 3.30



3.90 = 3.90

3.30 = 3.30







Whew that was long :D Hope it helps.