Question

Liam and evan are mixing paint. Liam uses 2 quarts of yellow paint and adds 3 1/4 jars of blue paint. Evan uses 1/2 quart of yellow paint and adds 5 1/2 jars of red paint. They end up with the same volume of paint. Write an equation to represent the situation.

Answer 1

To find an equation that represents the volume of paint mixed by Liam and Evan, we assume that 1 jar equals 1 quart. By adding the quarts of paint each person uses, we get the equation 2 + 3 1/4 = 1/2 + 5 1/2, meaning they both used the same total volume of paint.

Step-by-step explanation:

To find the equation that represents the situation, we need to equate the total volume of paint used by Liam to the total volume used by Evan. We know that Liam uses 2 quarts of yellow paint and adds 3 1/4 jars of blue paint. Evan, on the other hand, uses 1/2 quart of yellow paint and adds 5 1/2 jars of red paint. Assuming that 1 jar is equivalent to 1 quart, we can simply add the volumes for Liam and Evan:

Liam's total volume = 2 quarts (yellow) + 3 1/4 quarts (blue)

Evan's total volume = 1/2 quart (yellow) + 5 1/2 quarts (red)

Since they end up with the same volume of paint, we have the equation:

2 + 3 1/4 = 1/2 + 5 1/2

To solve for quarts, simplify both sides:

5 1/4 = 6

This equation represents the volumes of paint mixed by Liam and Evan.

Answer 2

The required equation is given by,

2 +
`\frac {13x}{4}` =
`\frac {1}{2} + \frac {11y}{2}`

Step-by-step explanation:

Let, each jar of Liam's paint contains x quarts of paint.

Then, Liam's solution contains,

2 +
`3\frac {1}{4} * x` quarts of paint or,

2 +
`\frac {13x}{4}` quarts of paint

and,

let, each jar of Evan's paint contains, y quarts of paint.

Then, Evan's solution contains,

`\frac {1}{2} + 5 \frac {1}{2} * y` quarts of paint or,

`\frac {1}{2} + \frac {11y}{2}` quarts of paint

now, according to the question,

the required equation is given by,

2 +
`\frac {13x}{4}` =
`\frac {1}{2} + \frac {11y}{2}`