SOLUTION: If the temperature on a Celsius scale is multiplied by three and added to two times the reading on a Fahrenheit scale, the result is 460. Five times the Celsius reading plus four t

Question 551293: If the temperature on a Celsius scale is multiplied by three and added to two times the reading on a Fahrenheit scale, the result is 460. Five times the Celsius reading plus four times the Fahrenheit reading is equal to 860. Find the temperature on each scale. Please help me!!!!!
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let C represent the reading on the Celsius scale and F represent the reading on the Fahrenheit scale.
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You are then told if you add 3 times C to 2 times F and the result is 460. In equation form write this as:
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Next you are told that if you add 5 times C to 4 times F the result is 860. In equation form this is:
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One of the ways to solve this is by the method of variable elimination. You can eliminate the variable F by multiplying both sides (all terms) of the first equation by 2. When you do that the first equation becomes:
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Write this above the second equation as follows:
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Next, subtract the second equation from the first equation in vertical columns. Note that the 4F in the first equation will be canceled by subtracting the 4F below it in the second equation. This eliminates the variable F. You are left with 6C minus 5C which is just C. And on the right side you are left with 920 minus 860 and this is 60. So what you have left is simply:
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This tells you that the answer for C is 60 degrees Celsius. Go back to either of the two equations and substitute 60 for C. Then solve for F. Since you can choose either equation, you can use:
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Substitute 60 for C and you have:
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Multiply the 5 times 60 to get 300 and the equation becomes:
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Eliminate the 300 from the left side by subtracting 300 from both sides. This subtraction results in:
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which simplifies to:
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Solve for F by dividing both sides of the equation by 4 to get:
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and dividing 4 into 560 results in the answer:
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So the reading on the Fahrenheit thermometer is 140 degrees.
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In summary the answers are C = 60 degrees and F = 140 degrees.
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Hope this helps you to understand the problem better.
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