A) The answer is x + y + z = 24 3x + 2y + z = 53 x = y + z
x - the number of swimmers in the first place y - the number of swimmers in the second place z - the number of swimmers in the third place
<span>1. The e-mail states that 24 individuals placed: x + y + z = 24 2. </span>First place earned 3 points, second place earned 2 points, and third place earned 1 point, <span>earning a combined total of 53 points: 3x + 2y + z = 53 3. </span><span> There were as many first-place finishers as second and third-place finishers combined: x = y + z
The system of three equations is: </span>x + y + z = 24 3x + 2y + z = 53 x = y + z
B) The answer is 12 swimmers in the first place 5 swimmers in the second place 7 swimmers in the third place
(i) x + y + z = 24 (ii) 3x + 2y + z = 53 (iii) x = y + z ______ Substitute y + z from the third equation into the first one: (i) x + y + z = 24 (iii) x = y + z ______ x + x = 24 2x = 24 x = 24 / 2 <u>x = 12</u> _____
x = y + z x = 12 y + z = 12 z = 12 - y
3x + 2y + z = 53 3 * 12 + 2y + (12 - y) = 53 36 + 2y + 12 - y = 53 2y - y + 36 + 12 = 53 y + 48 = 53 y = 53 - 48 <u>y = 5</u>
