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 y be the number of sports drinks. The first equation represents the total number of bottles:

x + y = 6

The second equation represents the total cost:

1.5x + 2.5y = 10

To solve for x and y, we can use substitution. Solving the first equation for y in terms of x:

y = 6 - x

Substituting this expression for y into the second equation:

1.5x + 2.5(6 - x) = 10

Expanding and simplifying the right side:

1.5x + 15 - 2.5x = 10

-x + 15 = 10

Subtracting 15 from both sides:

-x = -5

Dividing both sides by -1:

x = 5

Substituting this value for x back into y = 6 - x:

y = 6 - 5

y = 1

So Yui buys 5 bottles of water and 1 bottle of sports drink.

Explanation: