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 ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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       Log On


   

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: +10k%2B15c=360+
and +20%2B1%2F2c=220+
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) About Me  (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: +10k%2B15c=360+
and +20%2B1%2F2c=220+
------------------------------------------------------------------
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) About Me  (Show Source):
You can put this solution on YOUR website!
,b>
Good, +10k%2B15c=360+ -------------------------> EQN 1
we get, k=%28360-15c%29%2F10 ----------------------> EQN 2
But cross%2820%2B1%2F2c=220%29, we'll figure it out oks,
2 cats are gone, so --> k-2 right?
1/2 canaries are gone, so --> %281%2F2%29c right?
New value when they're gone, 220
Putting into eqn.
10%28k-2%29%2B15%281%2F2%29c=220 ------------------------> EQN 3
subst, EQN 2 in EQN 3:
10%28%28360-15c%29%2F10-2%29%2B15%281%2F2%29c=220
10%28%28360-15c-20%29%2F10%29%2B7.5c=220 Get LCD
cross%2810%29%28360-15c-20%29%2Fcross%2810%29%2B7.5c=220,
360-20-220=15c-7.5c, combine similar terms
120=7.5c ---> cross%28120%2916%2Fcross%287.5%29=cross%287.5%29c%2Fcross%287.5%29
c=16, TOTAL CANARIES BEFORE ESCAPING
For cats, go back EQN 2:
k=%28360-15%2A16%29%2F10=%28360-240%29%2F10
k=12, TOTAL CATS BEFORE ESCAPING
In doubt? Go back eqn 1:
10%2A12%2B15%2A16=360
120%2B240=360
360=360
Go back eqn 2,
10%2812-2%29%2B15%281%2Fcross%282%29%29%28cross%2816%298%29=220
10%2A10%2B15%2A8=220
100%2B120=220
220=220
Thank you,
Jojo