SOLUTION: Kiana and Jacobi each have a collection of identical red marbles and identical blue marbles. Kiana has a collection of 12 red marbles and 8 blue marbles weigh 70 grams. Jacobi coll
Question 1109449: Kiana and Jacobi each have a collection of identical red marbles and identical blue marbles. Kiana has a collection of 12 red marbles and 8 blue marbles weigh 70 grams. Jacobi collection of 20 red marble and 12 blue marbles weigh 110 grams. how much does each marble weigh? Answer by ikleyn(52788) (Show Source):
From the condition, you have this system of 2 equations
12*r + 8*b = 70 (1)
20*r + 12*b = 110 (2)
Use the Elimination method. For it, multiply eq(1) by 5 (both sides). Multiply eq(2) by 3 (both sides). You will get
60*r + 40*b = 350 (1')
60*r + 36*b = 330 (2')
Now subtract eq(2') from eq(1') (both sides). The terms "60*r" will cancel each other. (It is how the Elimination method works).
You will get a single equation for only one unknown
40b - 36b = 350 - 330
4b = 20 ====> b = = 5.
Then from eq(1)
12r + 8*5 = 70 ====> 12r = 70-40 = 30 ====> r = = 2.5.
Answer. Red marble weights 2.5 grams. Blue marble weights 5 grams.
Check. Checking is a necessary part of the solution.
Make checking on your own.
Solved. // On the way, you learned on how the Elimination method works.
