SOLUTION: Andrew bought some apples and pears. The ratio of the number of apples bought to the number of pears bought was 7:4. He spent $61.20. He paid $22.80 more for the apples than the pe

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Andrew bought some apples and pears. The ratio of the number of apples bought to the number of pears bought was 7:4. He spent $61.20. He paid $22.80 more for the apples than the pe      Log On


   

Question 1210397: Andrew bought some apples and pears. The ratio of the number of apples bought to the number of pears bought was 7:4. He spent $61.20. He paid $22.80 more for the apples than the pears. Each apple was $0.30 more than each pears.
(a) How much did he spend on the pears?
(b) How many pears did he buy?
Found 4 solutions by josgarithmetic, ikleyn, greenestamps, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
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This is not very neat and much likely not the best way, but this should work. 
          PRICE    QUANTY    COST

Apple     p+0.3     7x      7x(p+0.3)

Pear       p        4x      4x*p

Totals                      61.20

and too, the 22.8 dollars difference
system%287x%28p%2B0.3%29-4xp=22.8%2C7x%28p%2B0.3%29%2B4xp=61.2%29

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Andrew bought some apples and pears. The ratio of the number of apples bought to the number of pears bought was 7:4.
He spent $61.20. He paid $22.80 more for the apples than the pears. Each apple was $0.30 more than each pears.
(a) How much did he spend on the pears?
(b) How many pears did he buy?
~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let A be the amount he spent for apples.

Let P be the amount he spent for pears.


From the problem, we have these two equations

    A + P = 61.20,    (1)

    A - P = 22.80.    (2)


To find P, subtract equation (2) from equation (1).  You will get

    2P = 61.20 - 22.80

    2P = 38.4,  P = 38.4/2 = 19.2.


Thus, Andrew spent $19.20 for pears.  It is the answer for question (a).


From this, we conclude that Andrew spent  $61.20 - $19.20 = $42.00 for apples.



                   Now we start solving (b).



Andrew has 7n apples and 4n pears.  The number 'n' is unknown, and we want to find it.


The price for one apple is  42%2F%287n%29 = 6%2Fn.


The price for one pear is  19.2%2F%284n%29 = 4.8%2Fn.


The difference equation for price is

    6%2Fn - 4.8%2Fn = 0.3  dollars.


Simplify and find 'n'

    1.2%2Fn = 0.3,

    n = 1.2%2F0.3 = 4.


So, Andrew bought  7n = 7*4 = 28 apples and 4n = 4*4 = 16 pears.


It is the answer to question (b).

All questions are answered and the problem is solved completely.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


There are many ways you could set up this problem for solving. I looked briefly at a few different ways before choosing a method that looked as if it would be relatively easy. I would hope that other tutors might come to you with different solutions.

He spent a total of $61.20; and he spent $22.80 more for the apples than for the pears.

let a = cost of the apples
let p = cost of the pears

a%2Bp=61.20 the total cost was $61.20
a-p=22.80 the cost of the apples was $22.80 more than the cost of the pears

Solve the pair of equations by adding the two equations to solve for a and then use that number to find p.

2a=84.00
a=42.00
p=42.00-22.80=19.20

The total cost of the apples was $42; the total cost of the pears was $19.20.

The ratio of the number of apples to the number of pears was 7:4. So

let 7x = number of apples
then 4x = number of pears

Find the cost of x apples and the cost of x pears:

7x=42
x=6
The cost of x apples is $6.

4x=19.20
x=4.80
The cost of x pears is $4.80.

The cost of x apples is $6 - $4.80 = $1.20 more than the cost of x pears. Each apple costs $0.30 more than each pear, so x = $1.20/$0.30 = 4.

The cost of x=4 apples is $6, so the cost of each apple is $6/4 = $1.50.

The cost of x=4 pears is $4.80, so the cost of each pear is $4.80/4 = $1.20.

Check the results we have with the original given information:

He bought 7x = 28 apples at $1.50 each for a total of 28($1.50) = $42.00.
He bought 4x = 16 pears at $1.20 each for a total of 16($1.20) = $19.20.
The total he spent was $42.00+$19.20 = $61.20.

Looks good. Now answer the questions that were asked.

(a) How much did he spend on the pears?
ANSWER: $19.20

(b) How many pears did he buy?
ANSWER: 16

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Andrew bought some apples and pears. The ratio of the number of apples bought to the number of pears bought was 7:4. He spent $61.20. He paid $22.80 more for the apples than the pears. Each apple was $0.30 more than each pears.
(a) How much did he spend on the pears?
(b) How many pears did he buy?

Let multiplicative factor be x
As ratio of apples to pears is 7:4, number of apples and pears purchased = 7x and 4x, respectively

Let amount spent on pears be p
Since $22.80 more was spent on apples than pears, then amount spent on apples = p + $22.80
A total of $61.20 was spent, so we then have: p + p + 22.8 = 61.2
                                                        2p = 61.2 - 22.8
                                                        2p = 38.4
                        p, or amount spent on pears = highlight_green%2838.4%2F2+=+highlight%28%22%2419.20%22%29%29 

Since $19.20 was spent on “4x” pears, then cost of each pear = 19.2%2F%284x%29+=+4.8%2Fx
As $19.20 was spent on pears, $61.20 - $19.20, or $42 was spent on “7x” apples, and so, each apple cost 42%2F%287x%29+=+6%2Fx
Now, since each apple was $0.30 more than each pear, we get: 6%2Fx+=+.3+%2B+4.8%2Fx  
                                                             6 = .3x + 4.8 ---- Multiplying by LCD, x 
                                                       6 - 4.8 = .3x
                                                           1.2 = .3x                                                             
                            x, or multiplicative factor = 1.2%2F.3+=+12%2F3+=++4

Number of pears purchased: 4x = 4(4) = 16