SOLUTION: In a local pet store , the cats sell for $10 each and the canaries sell for $15 each. the total value was $360. one night the shop owner forgot to close the cages. 2 cats and half
Algebra.Com
Question 162620: In a local pet store , the cats sell for $10 each and the canaries sell for $15 each. the total value was $360. one night the shop owner forgot to close the cages. 2 cats and half of the canaries are gone. if the total value is now $220, how many of each were present before escape?
I was asked to find the solution by writing and solving a system of 2 linear equations.
so far i have that: k= number of cats and c= number of canaries
And what i think the equations might be:
and
Am i correct and if not how can i modify my equations to solve the equation easier? thanks.
Found 2 solutions by stanbon, jojo14344:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In a local pet store , the cats sell for $10 each and the canaries sell for $15 each. the total value was $360. one night the shop owner forgot to close the cages. 2 cats and half of the canaries are gone. if the total value is now $220, how many of each were present before escape?
I was asked to find the solution by writing and solving a system of 2 linear equations.
so far i have that: k= number of cats and c= number of canaries
And what i think the equations might be:
and
------------------------------------------------------------------
1st Value Equation: 10k + 15c = 360
2nd Value Equation: 10(k-2) + 15(c/2) = 220
--------------------------------
Rewrite for elimination:
10k + 15c = 360
20k + 15c = 480
-------------------
10k = 120
k = 12 (original # of cats)
-------------------
10*12 + 15c = 360
15c = 240
c = 16 (original # of canaries)
====================================
Cheers,
Stan H.
Answer by jojo14344(1513) (Show Source): You can put this solution on YOUR website!
,b>
Good, -------------------------> EQN 1
we get, ----------------------> EQN 2
But , we'll figure it out oks,
2 cats are gone, so --> right?
1/2 canaries are gone, so --> right?
New value when they're gone,
Putting into eqn.
------------------------> EQN 3
subst, EQN 2 in EQN 3:
Get LCD
,
, combine similar terms
--->
, TOTAL CANARIES BEFORE ESCAPING
For cats, go back EQN 2:
, TOTAL CATS BEFORE ESCAPING
In doubt? Go back eqn 1:
Go back eqn 2,
Thank you,
Jojo
RELATED QUESTIONS
In one day, a store sold 22 lamps. The larger lamps sell for $20 and the smaller lamps... (answered by mananth)
A pet shop buys a litter of puppies for $160. They sell all but four of the puppies. They (answered by edjones)
A store had a sale on t–shirts, during which they sold 186 t–shirts in three sizes,... (answered by josmiceli)
15.Candy bars were priced at .50 each but did not sell. Then the price was reduced and... (answered by Deina,richwmiller)
A pet store has a total of 35 dogs,cats,and rabbits. The number of rabbits is 1 more than (answered by htmentor)
A pet store has a total of 35 dogs,cats,and rabbits. the number pf rabbits is 1 more than (answered by ankor@dixie-net.com)
Pete and Repeat are brothers. Of course with names like Pete and Repeat they usually... (answered by solver91311)
The Audio Outlet purchased 60 cassette recorders, gave away three in a contest, and sold... (answered by ankor@dixie-net.com)
shawna and kali both work at the same pet store on monday shawna counts 52 birds and cats (answered by josmiceli)