Question

Rachel is at a cafe buying drinks for her friends. Some of them want coffee, while others wants tea. At this particular cafe, a regular cup of coffee costs $4 and regular of black tea cost $3. If she buys 7 drinks for a total cost of $26, how many of each type of drink did she purchase?​

Answer 1

Rachel bought 5 cups of coffee (x = 5) and 2 cups of black tea (y = 2).

Explanation:

Let's assume Rachel bought x cups of coffee and y cups of black tea. According to the given information, the cost of a cup of coffee is $4, and the cost of a cup of black tea is $3. We can set up the following equations based on the total cost:4x + 3y = 26 ---(1) (Total cost equation)

x + y = 7 ---(2) (Total number of drinks equation)To solve this system of equations, we can use substitution or elimination method. Let's use the elimination method to solve the equations: Multiply equation (2) by 3 to make the coefficients of y in both equations equal:3(x + y) = 3(7)

3x + 3y = 21 ---(3)Now, subtract equation (3) from equation (1) to eliminate y:4x + 3y - (3x + 3y) = 26 - 21

4x + 3y - 3x - 3y = 5

x = 5Substitute the value of x = 5 into equation (2) to find y:5 + y = 7

y = 7 - 5

y = 2