How do I convert this to an algebra equation?

Question

A pet shop has 100 puppies, kittens and turtles. A puppy costs $30, a kitten costs $20 and a turtle costs $5. If there are twice as many kittens as puppies, and if the stock in worth $1,050, how many of each type of animal is there? I know the answer, but I did it by guessing,. I don't know how to write this as an equation

Answer 1

Hi Denise F.

10 puppies

20 kittens

70 turtles

You can use a system of equations and substitution to set up the problem in terms of one variable please see below

Let x = puppies

Let y = kittens

Let z = turtles

If there are twice as many kittens as puppies then

y = kittens = 2(puppies) = 2x

y = 2x

We can substitute 2x for y in our equations

For our Equations we have two

Total Stock Equation 1

x + 2x + z = 100

We know puppies cost 30 each, kittens cost $20 and turtles cost $5 each

Total Worth of stock Equation 2

30x + 20(2x) + 5z = 1050

When we combine like terms

Equation 1

3x + z = 100

with z = 100 -3x (this puts z in terms of x)

Equation 2

30x + 40x + 5z = 1050

70x + 5z = 1050

We now have two equations in two unknowns but we can again use substitution to put everything in terms of x in Equation 2

70x + 5(100 -3x) = 1050

70x + 500 - 15x = 1050

Combine like terms again

55x + 500 = 1050

Subtract 500 from both sides of the equation

55x = 550

Divide both sides by 55

x = 10

Since we already know from the previous substitutions

y = 2x = 20

z = 100 - 3x = 70

We have 10 puppies, 20 kittens and 70 turtles

Checking in the original equations

x + y + z = 10 + 20 + 70 = 100

30(10) + 20(20) + 5(70) = 300 + 400 + 350 = 1050

I hope this helps it can also be done by Elimination

Answer 2

30P + 20K + 5T = 1050

K=2P

P+K+T =100

5P+5K+5T = 500

subtract that from the 1050 equation to get

25P +15K = 550

change K to 2P

25P + 15(2P) = 550

55P = 550

P =10 puppies

K=20 kittens

T = 100-30 = 70 turtles

30(10) + 20(20) + 70(5) = 1050

300 +400 + 350 = 1050

Answer 3

p represents number of puppies

2p represents the number of kittens

100 - 3p represents the number of turtles

($30)p + ($10)(2p) + ($5)(100 - 3p) = 1050

Can you solve for p and answer?