0

# Danielle went to a pet store and bought 7 dogs and 5 cats for 760. If dogs cost twice as much as cats what is the cost of each?

whats the system of equation for it

### 1 Answer by Expert Tutors

Ami P. | Doctorate-level scientist available for science tutoring Doctorate-level scientist available for ...
5.0 5.0 (3 lesson ratings) (3)
0
X = dogs and Y = cats

Equation 1: 7X + 5Y = 760
Equation 2: X = 2Y (since a dog is twice as expensive as a cat in this scenario)

To solve this sort of problem, you need to rewrite equation 1 so that it contains only one unknown variable using equation 2 as a conversion factor.
So equation 1 can be rewritten two different ways that lead to the correct solutionâ€¦â€¦

Method #1: Express the value of dogs (X) in terms of the value of cats (Y)
So equation 1 becomes 7(2Y) + 5Y = 760
which simplifies to 14Y + 5Y = 760
and then simplifies again to 19Y = 760
Divide each side of the equation by 19 to find the value of Y. Y = \$40
Now use the known value of Y to determine the unknown value of X by plugging it into either equation 1 or equation 2. X= \$80

Method #2: Express the value of cats (Y) in terms of the value of dogs (X)
By dividing both sides of equation 2 by 2, we determine that Y = 0.5X
So equation 1 becomes 7X + 5(0.5X) = 760
which simplifies to 7X + 2.5X = 760
and then simplifies again to 9.5X = 760
Divide each side of the equation by 9.5 to find the value of X. X = \$80
Now use the known value of X to determine the unknown value of Y by plugging it into either equation 1 or equation 2. Y = \$40