SOLUTION: 1) The music teacher at your school buys and sells fresh fruit to help raise funds to support the school concert band. One day the total order for bags of oranges and bags of apple

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 1) The music teacher at your school buys and sells fresh fruit to help raise funds to support the school concert band. One day the total order for bags of oranges and bags of apple      Log On


   

Question 202047: 1) The music teacher at your school buys and sells fresh fruit to help raise funds to support the school concert band. One day the total order for bags of oranges and bags of apples cost $33.00 exactly. If 15 bags of fruit were purchased, how many bags contained oranges?
BY THE BAG
ORANGES $5.00
APPLES $2.00
2)The Outdoors Club held a car wash to raise money. They washed cars for $5 each and vans for $7 each. They washed 45 vehicles and made $243. How many of each type of vehicle did they wash?
3)One type of granola is 30% fruit, and another type is 15% fruit. What mass of each type of granola should be mixed to make 600g of granola that is 21% fruit?
4). One lawn fertilizer is 24% nitrogen and another is 12% nitrogen. How much of each fertilizer should be mixed to obtain 100kg of fertilizer that is 21% nitrogen?
plzzzz help! thanks!


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two problems to get you going in the right direction.



# 1

Let

x = number of bags of oranges purchased
y = number of bags of apples purchased


Because "15 bags of fruit were purchased", we know that x%2By=15

Since the oranges are $5 a bag and the apples are $2 a bag, and a total cost was $33, this means that 5x%2B2y=33



So we have the system of equations:


system%28x%2By=15%2C5x%2B2y=33%29


x%2By=15 Start with the first equation.


y=15-x Subtract x from both sides.


y=-x%2B15 Rearrange the terms.


-------------------------------------------


5x%2B2%28-x%2B15%29=33 Now plug in y=-x%2B15 into the second equation.


5x-2x%2B30=33 Distribute.


3x%2B30=33 Combine like terms on the left side.


3x=33-30 Subtract 30 from both sides.


3x=3 Combine like terms on the right side.


x=%283%29%2F%283%29 Divide both sides by 3 to isolate x.


x=1 Reduce.


-------------------------------------------


Since we know that x=1, we can use this to find y.


x%2By=15 Go back to the first equation.


1%2By=15 Plug in x=1.


y=15-1 Subtract 1 from both sides.


y=14 Combine like terms on the right side.



=============================================================

Answer:



So the solutions are x=1 and y=14.


This means that 1 bag of oranges and 14 bags of apples were purchased





# 2


Let


x = number of cars washed
y = number of vans washed


Because "They washed 45 vehicles", we know that x%2By=45


Also, since "They washed cars for $5 each and vans for $7 each" and "made $243", we get that 5x%2B7y=243


So we have the system of equations:


system%28x%2By=45%2C5x%2B7y=243%29


x%2By=45 Start with the first equation.


y=45-x Subtract x from both sides.


y=-x%2B45 Rearrange the terms.


-------------------------------------------


5x%2B7%28-x%2B45%29=243 Now plug in y=-x%2B45 into the second equation.


5x-7x%2B315=243 Distribute.


-2x%2B315=243 Combine like terms on the left side.


-2x=243-315 Subtract 315 from both sides.


-2x=-72 Combine like terms on the right side.


x=%28-72%29%2F%28-2%29 Divide both sides by -2 to isolate x.


x=36 Reduce.


-------------------------------------------


Since we know that x=36, we can use this to find y.


x%2By=45 Go back to the first equation.


36%2By=45 Plug in x=36.


y=45-36 Subtract 36 from both sides.


y=9 Combine like terms on the right side.




=============================================================

Answer:


So the solutions are x=36 and y=9.


This means that they washed 36 cars and 9 vans