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A mobile service provider charges 11 dollars plus four dollars per minute for long-distance calls, whereas another provider charges 26 dollars plus one dollar 50 per minute.
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Write an equation that represents the number of minutes for which the two providers will charge the same amount and then solve it.
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The total charge for each mobile service provider is equal to their fixed cost plus the cost of the long-distance calls.
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As we’re forming an equation, we’ll let the number of minutes spent on long-distance calls be equal to 𝑥.
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The first mobile service provider charges 11 dollars — that’s their fixed cost — plus four dollars per minute.
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Their total charge will therefore be 11 plus four multiplied by 𝑥: 11 plus four 𝑥.
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The second mobile service provider charges 26 dollars plus one dollar 50 per minute.
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Their total charge will therefore be equal to 26 dollars for the fixed cost plus 1.5 multiplied by 𝑥: 26 plus 1.5𝑥.
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As the charges for the two mobile service providers are the same for this number of minutes, we can write this as an equation: 11 plus four 𝑥 is equal to 26 plus 1.5𝑥.
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Now, we want to solve our equation.
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The first step is to subtract 11 from each side.
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This gives four 𝑥 is equal to 15 plus 1.5𝑥.
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Now, there’re 𝑥 terms on both sides and we would like to group them all on one side of the equation.
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So the next step is to subtract 1.5𝑥 from both sides.
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This gives 2.5𝑥 is equal to 15.
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To find the value of 𝑥, we need to divide both sides of the equation by 2.5.
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𝑥 is equal to 15 over 2.5.
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Now, we’re currently being asked to divide by a decimal, which is quite a tricky thing to do.
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So in order to make this simpler, I’m going to multiply both the numerator and denominator of the fraction by two.
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This gives an equivalent fraction as I’ve done the same operation to both the numerator and the denominator.
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But now, it’s a much more straightforward division: 30 divided by five.
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This is equal to six.
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So the equation that we were asked to form to represent the number of minutes for which the two providers will charge the same amount is 11 plus four 𝑥 is equal to 26 plus 1.5𝑥.
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The solution to this equation is 𝑥 is equal to six, meaning that for six minutes, the two providers will charge the same amount.