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The sum of a​ student's three scores is 203. If the first is 14 points more than the​ second, and the sum of the first two is 2 more than twice the​ third, what was the first​ score.

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1 Answer

3 votes

Answer:

75

Explanation:

Given relations between three scores that total 203, you want to know the first score.

Setup

The equations for scores a, b, c can be written ...

a + b + c = 203

a - b = 14

a + b - 2c = 2

where 'a' is the fist score.

Solution

We can write expressions for b and c using the last two equations.

b = a -14

2c = a +b -2 = a +(a -14) -2 = 2a -16 ⇒ c = a -8

Substituting into the first equation gives ...

a +(a -14) +(a -8) = 203

3a = 225 . . . . . . add 22

a = 75 . . . . . . . . divide by 3

The first score was 75.

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Additional comment

A calculator can solve the three equations shown in the setup, giving all three answers as quickly as the coefficients can be entered.

(a, b, c) = (75, 61, 67)

The sum of a​ student's three scores is 203. If the first is 14 points more than the-example-1
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