SOLUTION: almaz has taken two tests. her average score is 7 out of ten. the product of her score is 45. what did she score in each test

Question 1132777: almaz has taken two tests. her average score is 7 out of ten. the product of her score is 45. what did she score in each test

Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let a represent the first number and b represent the second number.

since the average score is 7, you get (a + b) / 2 = 7
multiply both sides of this equation by 2 to get a + b = 14

the produce of her scores is 45 means that a * b = 45.

you have 2 equations that need to be solved simultaneously.

they are a + b = 14 and a * b = 45

solve for a in the second equation to get a = 45 / b.

replace a with 45 / b in the first equation to get 45 / b + b = 14

multiply both sides of this equation by b to get 45 + b^2 = 14b

subtract 14b from both sides of this equation and arrange the terms in descending order of degree to get b^2 - 14b + 45 = 0

factor this quadratic equation to get (b - 9) * (b - 5) = 0

solve for b to get b = 9 or b = 5.

the average of these 2 numbers is (9 + 5) / 2 = 7.

the product of these 2 number is 9 * 5 = 45.

solution looks good.

solution is that she scored 9 out of 10 in one test and 5 out of 10 in the other test.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Since there are only two test scores, with an average of 7 out of 10, let the two scores be 7+x and 7-x. Then, since the product of her two test scores is 45,

The two test scores are 7+x=9 and 7-x=5.

Of course, if an algebraic solution is not required, the question can be answered easily by trial and error -- what two numbers whose product is 45 have an average of 7?
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