Video: Evaluating a Variable in a Given Linear Equation given the Values of Other Variables

The profit equation for a small business selling π‘₯ of item A and 𝑦 of item B is 𝑝 = 3π‘₯ + 4𝑦. Find 𝑦 when 𝑝 = $453 and π‘₯ = $75.

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Video Transcript

The profit equation for a small business selling π‘₯ of item A and 𝑦 of item B is 𝑝 is equal to three π‘₯ plus four 𝑦. Find 𝑦 when 𝑝 is equal to 453 dollars and π‘₯ equals 75.

We begin this question by considering the equation 𝑝 is equal to three π‘₯ plus four 𝑦. We’re told that 𝑝 is equal to 453 dollars. π‘₯ is equal to 75. So we need to multiply this by three. Our equation becomes 453 is equal to three multiplied by 75 plus four 𝑦. Three multiplied by 75 is 225. We can then subtract this from both sides of the equation. This gives us four 𝑦 is equal to 228. Dividing both sides of this equation by four will give us our value for 𝑦. 228 divided by four is 57. We can therefore conclude that selling 75 of item A and 57 of item B gives a profit of 453 dollars.

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