Video: Writing and Solving One-Variable Equations

One telephone service provider charges $1 plus an additional $0.50 per minute for international calls, whereas another provider charges $4 plus an additional $0.25 per minute. Write and solve an equation to find the call length for which the two telephone service providers would charge the same amount.

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Video Transcript

One telephone service provider charges one dollar plus an additional 50 cents per minute for international calls, whereas another provider charges four dollars plus an additional 25 cents per minute. Write and solve an equation to find the call length for which the two telephone service providers would charge the same amount.

So one provider charges one dollar plus an additional 50 cents per minute, where the other charges four dollars plus an additional 25 cents per minute. So let’s go ahead and let the variable 𝑥 represent the number of minutes that the caller would be on the phone.

So let’s begin with the first telephone service provider: one dollar plus an additional 50 cents per minute so times 𝑥. And we wanna find the call length for which the two telephone service providers would charge the same amount. So we want them to be equal. So let’s use an equal sign. And the other service provider charges four dollars plus an additional 25 cents per minute — so 0.25𝑥.

Now, let’s go ahead and solve for 𝑥, which will be the number of minutes which would be the call length. So we will begin by subtracting one from both sides of the equation and we have 0.50𝑥 equals three plus 0.25𝑥. Let’s put the 𝑥s together. So let’s go ahead and subtract 0.25𝑥 from both sides of the equation. So we have 0.25𝑥 equals three. So to eliminate the 0.25 so we can get 𝑥 by itself, let’s divide both sides of the equation by 0.25. And we find that 𝑥 equals 12.

So our equation to find the call length for which the two telephone service providers would charge the same amount would be one plus 0.50𝑥 equals four plus 0.25𝑥. And we would solve this and find that the call length for which the two telephone service providers will charge the same amount will be 12 minutes.

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