Question

Coworkers Jan and Richard purchase lunch from food truck. Jan buys 1 beef taco and 2 fruit cups for $5.25. Richard buys 3 beef tacos and 1 fruit cup for $8.25. Find the price of each item (beef taco, fruit cup)

Answer 1

Given:

Jan buys 1 beef taco and 2 fruit cups for $5.25.

Richard buys 3 beef tacos and 1 fruit cup for $8.25.

Required:

We need to find the price of each item beef taco and fruit cup.

Step-by-step explanation:

Let x be the price of a beef taco.

Let y be the price of a fruit cup.

The cost of 1 beef taco and 2 fruit cups = $ 5.25

`x+2y=5.25`

Subtract 2y from both sides of the equation.

`x+2y-2y=5.25-2y`
`x=5.25-2y`

The cost of 3 beef tacos and 1 fruit cup = $ 8.25

`3x+y=8.25`

`Substitute\text{ }x=5.25-2y\text{ in the equation.}`

`3(5.25-2y)+y=8.25`
`15.75-6y+y=8.25`
`15.75-5y=8.25`

Add 5y- 8.25 to both sides of the equation

`15.75-5y+5y-8.25=8.25+5y-8.25`
`7.5=5y`

Divide both sides by 5.

`(7.5)/(5)=(5y)/(5)`
`1.5=y`

`Substitute\text{ }y=1.5\text{ in the equation }x=5.25-2y.`

`x=5.25-2(1.5)`
`x=2.25`

Final answer:

The price of a beet taco is $ 2.25.

The price of a fruit cup is $ 1.50.