Answer:
Equations:
a + b = 19
a = b + 2
a = Money that spent Laura
b = Money that spent Laureen
then:
(b+2) + b = 19
2b + 2 = 19
2b = 19-2
2b = 17
b = 17/2
b = 8.5
a = b + 2
a = 8.5 + 2
a = 10.5
Check:
10.5 + 8.5 = 19
He is incorrect because each number is in a different place and those different places are worth more or less than the other places
We will start with our guess of 12, since 12*2 = 24.
Divide 24 by 12; 24/12=2. Average this answer with our guess: (12+2)/2=7. This is our new guess.
24/7=3.428571429. Average this with our guess of 7: (3.428571429+7)/2=5.214285715. This is our new guess.
24/5.214285715=4.602739726. Averaging with our guess: (4.602739726+5.214285715)/2=4.90851272. New guess!
24/4.90851272=4.889464766. Averaging with our guess: (4.889464766+4.90851272)/2=4.898988743. New guess! You can see as we go through our guesses are closer and closer to the same number...)
24/4.898988743=4.898970228. Averaging: (4.898970228+4.898988743)/2=4.898979486. At this point our answer is the same every time down to the hundred-thousandth. Our estimate to the nearest hundredth would be 4.90.
The first column is the ratio you start with. The next column in the table should be the reduced fraction. To properly reduce a fraction, you divide the same number on the top and bottom of the fraction. Melody instead subtracted 1 in the top and bottom of the fraction to reduce it. She should have divided the top and bottom by 2 to get the second column of 1 pound of turkey and 3 people served.
The final column is designed to be the answer to the initial question of how many people are fed by 15 pounds of ground turkey. Starting with column 2 (the reduced ratio of 1/3), multiply the top by 15 to get 15 pounds of ground turkey. Then do the same to the bottom of the fraction. 3 x 15 = 45 people fed.
So the table should have been
Pounds of turkey 2 1 15
People served 1 3 45
Melody's overriding error was in believing that adding or subtracting numbers to both the top and bottom of a ratio/fraction keep its value the same. Instead, only multiplying or dividing the top and bottom by the same number creates an equivalent fraction.
