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igor_vitrenko [27]
2 years ago
8

On the first of three tests Kayla scored 72points. On the third test her score was 1 point more than on the second. Her average

on the three tests was 83. What was her scores on the seconds and third testes
Mathematics
1 answer:
Kitty [74]2 years ago
5 0

Answer:

The answer to your question is:

first test = 72

second test = 88

third test = 89

Step-by-step explanation:

Data

First test = 72 points

Second test = x

Third test = x + 1

Average of the three test = 83

Process

       (First test  + Second test  + Third test) / 3  = 83

       ( 72 + x + x +1 ) / 3 = 83

        73 + 2x = 3(83)

        73 + 2x = 249

        2x = 249 - 73

        2x = 176

        x = 176 / 2 = 88   second test

        third test = x + 1 = 88 + 1  = 89

   

         

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Answer:

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Step-by-step explanation:

There are a number of ways to solve mixture problems like this. Some are simple enough you can almost write down the answer. One I like uses a diagram to help you find the ratios of the components of the mix. You can do the same thing with a formula (without the diagram).

The basic idea is that you compute a ratio between two differences. The numerator is the difference between the average interest rate and the lower interest rate. Here, the average interest rate is 2700/30,000 = 0.09 = 9%. Then the numerator is 9% -8.5% = 0.5%

The denominator is the difference between the two interest rates of the investments: 10% -8.5% = 1.5%. And the ratio of these two values is ...

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Then the remaining amount, $20,000, was invested at 8.5%.

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If you would prefer an equation, you can let x represent the amount invested at the higher rate. (That is the most convenient assignment of variables, as it keeps all of the numbers positive.) Then (30,000 -x) is the amount invested at the lower rate. The total amount of interest is ...

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We have purposely left the expression unevaluated so that you can compare it to the math we described above. If you factor out 30,000 from the numerator of this fraction, you see the ratio that we described in words:

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