SOLUTION: Supplying a sheep to a family costs AU$50 and a bee hive costs AU$35. If there were 24 gifts totaling AU$990, how many of each were bought? What would be the benefit of supplying

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Supplying a sheep to a family costs AU$50 and a bee hive costs AU$35. If there were 24 gifts totaling AU$990, how many of each were bought? What would be the benefit of supplying      Log On


   

Question 1195948: Supplying a sheep to a family costs AU$50 and a bee hive costs AU$35. If there
were 24 gifts totaling AU$990, how many of each were bought? What would be the
benefit of supplying a sheep or bee hive to a family?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Not clear, "24 gifts". Is this supposed to be total of the number of sheep and hives ?

h, hives
x, sheep
system%2850x%2B35h=990%2Cx%2Bh=24%29
If this makes good sense, then just simplify and solve.

A possible path:
system%28%281%2F5%29%2850x%2B35h%29=%281%2F5%29%28990%29%2Cx%2Bh=24%29

system%2810x%2B7h=198%2Cx%2Bh=24%29

system%2810x%2B7h=198%2C7x%2B7h=168%29----------------YOU FINISH!!

Answer by ikleyn(52818) About Me  (Show Source):
You can put this solution on YOUR website!
.
Supplying a sheep to a family costs AU$50 and a bee hive costs AU$35. If there were 24 gifts totaling AU$990,
how many of each were bought? What would be the benefit of supplying a sheep or bee hive to a family?
~~~~~~~~~~~~~~~


Written so inaccurately, this non-sensical mess of words is not a Math problem.

To future generations of students, who will read it, my advise is do not take it seriously.

This post does not deserve any serious consideration.



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


One formal algebraic method for solving....

x = # of $50 gifts
24-x = # of $35 gifts

The total cost was $990:

50%28x%29%2B35%2824-x%29=990
50x%2B840-35x=990
15x=150
x=10

ANSWER: x=10 $50 gifts; 24-x=14 $35 gifts

CHECK: 10(50)+14(35) = 500+490 = 990

A very different, less formal approach, using logical reasoning instead of formal algebra....

24 gifts all at $35 would cost $840; 24 all at $50 would cost $1200.
Consider the three costs 840, 990, and 1200 on a number line and observe/calculate that 990 is 150/360 = 5/12 of the way from 840 to 1200.
That means 5/12 of the 24 gifts, or 10 gifts, were the $50 gifts, making the number of $35 gifts 24-10 = 14.

ANSWER (again): 10 $50 gifts, 14 $35 gifts

The second question in your post is not math; I leave it to you to find a reasonable answer.