Six pears and three apples cost $3.90. Two pears and five apples cost $3.30.?
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.
Favorite Answer
2p+5a=3.30
multply 2nd equation by 3
6p+15a=9.90
subtract
12a=6
a=.50
Now substitute a in the first equation to get p.
6p+3*.50 = 3.90
6p=3.90-1.50
6p=2.40
p=.40
*
6p + 3a = 3.9
2p + 5a = 3.3
Multiple equation 2 by 3 to get 6p + 15a = 9.9
Subtract the two equations
6p + 15 a = 9.9
6p + 3a = 3.9
12a = 6, a = .5 substitute into either equation
6p + 1.5 = 3.9
6p = 3.9-1.5 = 2.4
p = .4 or 40 cents
verify
6 (.40) + 3(.5) = 2.4 + 1.5 = 3.9
2 (.40) + 5 (.50) = .80 + 2.50 = $3.30
6p + 3a = 3.90
2p + 5a = 3.30
Use whatever method you want to solve for p and a. Then add p and a together to get the cost of one of each.
Let equation 2) read 2p+5a=3.30
using simultaneous equation to solve
equation 1) 6p=3.90-3a
p=? etc
then place p in equation 2) to get cost of then do b.
hey can’t do everything for you rite
actually i’m surprised i remember this stuff
get one variable alone….6p+3a=3.90
You may divide the whole equation by 3
2p+a=1.30
a=1.30-2p
Substitute the results for a in the second equation
2p+5(1.30-2p)=3.30
2p+6.50-10p=3.30
-8p+6.50=3.30
-8p= -3.20
8p=.3.20
p=.40
Use the price of a pear to figure out the cost of an apple
6p+5a=3.90
6(.40)+5a=3.90
2.40+5a=3.90
5a=3.90-2.40
5a=1.50
a=.30
Check your work when done by substuting the values back into the oriignal equations
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