how much does the pear cost alone?

Question

If an apple & a pear cost 65 cents, a pear & a banana cost 50 cents, & an apple & a banana cost 55 cents, how much does the pear cost alone?

Answer 1

1.) a + p = 65
2.) b + p = 50
3.) a + b = 55

Add equations 1 and 2 up:
a + p + b + p = 115

Re-arrange
2p + a + b = 115

From equation 3 we know that a + b = 55
=> 2p + 55 = 115
=> 2p = 60
=> p = 30

A pear alone costs 30 cents.

Hope this helps.
________
* this is not the only way of solving this problem, but it is the easiest one.

Answer 2

well okie that' see here
a for apple
p for pear
b for banana

a + p =.65
p + b = .50
a + b = .55

how much is a pear......well

you would need to combine all 3 questions first......
which mean
if you want to solve for the pear

then this is what it would like next

p = .65 - a
p = .50 -b
a = .55 - b

combine .65 - a = .50- b because that would give you the price of the pear

but since you have a and b as part of the unknown it's hard for yout solve.....but you do know that a is equal to .55 - b

therefore you can put the equation as .65- (.55 - b) =.50 -b

Sound simplier now?!

Well now combine like terms.....
.65-.55+b = .50-b
.10 +b = .50 -b
.10-.50+b= -b
-.40= -b -b
-.40=-2b
b is euqal to .20

which mean the banana cost 20 cent and if you know banan cost 20 and that one banana and one pear total cost 50 cent.....then the pear would be .50-.20 would give you 30 that mean the pear is 30 cent

just something extra, and to find the amount for apple, you would take apple and a pear equal to 65 cent, and you know the pear is 30 cent now...therefore the apple is 35 cent, to make sure you did it right, tried to see if one apple and a banana is equal to 55 cent.....Am i right?

Conclusion

Apple cost 35 cent
Pear cost 30 cent
Banana cost 20 cent

hope this help

Answer 3

Let a, p, and b represent the cost of an apple, pear, and banana respectively. So from the information given:

1) a+p=65
2) p+b=50
3) a+b=55

Let's rearrange 1) and 3) to isolate p and b
1) a+p=65
4) p = 65 - a

3) a+b=55
5) b=55-a

Substitute 5) into 2)
2) p+b=50
p+(55-a)=50
6) p=a-5

Since both 4) and 6) have p=, we can equate them:
4) = 6)

a-5=65-a
2a=70
a=35

Now sub a into 1)
1) a+p=65
35+p=65
p=30

Therefore, the pear costs 30 cents.

Hope that helps!

Answer 4

if a = apple, b=pear, and c=banana, then
a+b=65
b+c=50
a+c=55
solve the first equation for b. b=65-a and substitue in one of the other equations. i picked the second equation to substitute. 65-a+c=50 add like terms, -a+c=-15. i then add this equation to the 3rd equation and solve simultaneously and get 2c=40 where c =20. i then plug 20 in for c and get b=30 and a=35. so the pear costs 30 cents

Answer 5

a = cost of an apple
b = cost of a banana
p = cost of a pear

a+p = 65
p+b = 50
a+b = 55

Subtract the last 2 equations and get
p-a = -5 or a = p+5
Sub into the first equation
p+5+p = 65
2p + 5 = 65
2p= 60
p =30
One pear cost 30 cents.

Answer 6

a+p = 65 <-- Eq1
p+b = 50 <-- Eq 2
a+b = 55 <-- Eq 3
Subtract Eq3 from Eq 1 getting:
p-b = 10 <-- Eq 4
Add Eq4 to Eq2 getting:
2p = 60
p = 30 cents = cost of pear alone.

Answer 7

$.30.
b/c apple+pear=$.65 [apple=35, pear=30],

banana+pear=$.50 [banana=20, pear=30],

apple+banana=$.55 [apple=35, banana=20].