Question

Yui is buying beverages for her friends. She buys a total of 6 bottles of water and sports drinks. Bottles of water cost $1.50 each, and sports drinks cost $2.50 each, she spends a total of $10. Write a system of equations to represent the information, and use substitution to determine how many of each type of drink yui buys

Answer 1

Let x be the number of bottles of water that Yui buys, and let y be the number of sports drinks she buys.

Since Yui buys a total of 6 bottles of water and sports drinks, we know that:

x + y = 6

We also know that each bottle of water costs $1.50 and each sports drink costs $2.50, and that Yui spends a total of $10. Therefore, we can write another equation based on the total cost:

1.5x + 2.5y = 10

We now have a system of two equations with two variables:

x + y = 6

1.5x + 2.5y = 10

To solve for x and y, we can use substitution. Rearranging the first equation, we get:

x = 6 - y

Substituting this expression for x into the second equation, we get:

1.5(6 - y) + 2.5y = 10

Expanding and simplifying, we get:

9 - 1.5y + 2.5y = 10

Combining like terms, we get:

y = 2

Substituting this value of y back into the equation x + y = 6, we get:

x + 2 = 6

Solving for x, we get:

x = 4

Therefore, Yui buys 4 bottles of water and 2 sports drinks.