Word problem im stuck

Question

Given a sports drink is $1.75 and a slice of pizza is $2.25

A person makes a purchase for $21.50. They purchased 3 more sports drinks than pizza. How many sports drinks did they purchase?

Answer 1

To solve this lets call sports drink as 'x' and slice of pizza as 'y'. Specifically they will be representing the amount of sports drinks and the number of slices pizza, respectively.

Sports Drink cost = 1.75x

Slice of Pizza cost = 2.25y

Total cost, based on the line that states that the person makes a purchase of 21.50:

1.75x + 2.25y = 21.50

You can multiply the equation by 100 to get rid of the decimals:

175x + 225y = 2150

Based on the statement that the person bought 3 more sports drinks than pizza, our second equation is:

x = y + 3

Our two equations:

175x + 225y = 2150

x = y + 3

Substitute for x in the first equation:

175x + 225y = 2150

175(y + 3) + 225y = 2150

Simplify the equation:

175(y + 3) + 225y = 2150

175y + 525 + 225y = 2150

400y +525 = 2150

Solve for y:

400y + 525 = 2150

400y + 525-525 = 2150-525

400y = 1625

y = 4.0625 which can be up-ed to 5, since you can not have half of items.

To find the value of x we can add 3 to 5:

x = y + 3

x = 5 + 3

x = 8

Check your work in the first original equation to see if the values work:

1.75(x) + 2.25y = 21.50

1.75(8) + 2.25(5) = 21.50

14.00 + 11.25 =22.25

25.25 does not equal 22.25

I have to say that something is not right about this problem. Please recheck the numbers and the problem itself. For the magic behind an equation is that if the problem and its content are correct, there should be no issue in getting the correct answers.