Question

The ratio of Christmas gifts you get to what your dog gets is 4:1. If you get 21 more gifts than your dog, how many gifts are yours and how many are your dog's?

Answer 1

To solve this problem, set up a ratio equation. Given the ratio of 4:1 and the fact that you get 21 more gifts than your dog, you can solve a system of equations to find the number of gifts for each. The solution is that you have 28 gifts and your dog has 7 gifts.

Step-by-step explanation:

To solve this problem, we can set up a ratio equation based on the information given. Let's say the number of gifts you get is represented by x, and the number of gifts your dog gets is represented by y. The given ratio is 4:1, which means for every 4 gifts you get, your dog gets 1 gift. We're also told that you get 21 more gifts than your dog, so we can write the equation as: x/y = 4/1

Since you get 21 more gifts than your dog, we can write another equation as: x = y + 21

Now we can solve the system of equations:

1. Substitute the value of x from the second equation into the first equation: (y + 21)/y = 4/1
2. Cross multiply: 1*(y + 21) = 4*y
3. Simplify: y + 21 = 4y
4. Combine like terms: 3y = 21
5. Divide both sides by 3: y = 7
6. Substitute the value of y back into the second equation: x = 7 + 21
7. Simplify: x = 28

Therefore, you have 28 gifts and your dog has 7 gifts.