SOLUTION: problem 1: Mrs.Davidson bought some apples and oranges for a total of $4.10.The cost of an orange is 50 cents which is 10 cents more than the cost of an apple.If there were a tota

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Question 1092059: problem 1:
Mrs.Davidson bought some apples and oranges for a total of $4.10.The cost of an orange is 50 cents which is 10 cents more than the cost of an apple.If there were a total 0f 9 fruits,find the number of apples and number of oranges Mrs.Davidson bought.
Found 3 solutions by Fombitz, ikleyn, greenestamps:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!

1.
and
2.
Multiply 2 by 5 and subtract from 1,


Check your problem setup.
The number of apples and oranges must be positive integers.
Please check and repost.

Answer by ikleyn(52848)   (Show Source): You can put this solution on YOUR website!
.
From the condition, the cost of one orange is 50 cents and the cost of one apple is 50 - 10 = 40 cents.


Let x be the number of apples.

40x + 50*(9-x) = 410  cents  ====>  40x + 450 - 50x = 410  ====>  -10x = 410-450 = -40  ====>  x = 4.


Answer.  4 apples and 9-4 = 5 oranges.


There are 3 (three) ways to solve this problem. 

    1.  Writing the system of 2 equations in two unknowns.

    2.  Using one equation and one unknown (it is what I did in my post)

    3.  To solve the problem MENTALLY, without using equations.

        It is what the tutor @greenestamps did in his post.

See the lessons
    - Problem on two-wheel and three-wheel bicycles,
    - Problem on animals at a farm  and
    - Problem on pills in containers
in this site, where similar problems were solved using all three methods.


Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

How about an informal solution....

If all 9 fruits were oranges, the cost would be 9 times 50 cents, a total of $4.50.

But the total cost was $4.10, which is 40 cents less than $4.50.

Since each apple costs 10 cents less than each orange, and since $4.10 is 40 cents less than $4.50, the number of apples must be 40/10 = 4.
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