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