Abag contains purple marbles and red marbles, 114 in total. the number of purplemarbles is 6 more than 5 times the number of red marbles. how many purplemarbles are there?

Explanation:

Givens

Purple marbles = P

Red marbles = R

Equations

P + R = 114

P = 5*R + 6

Solution

Put the second equation into the first.

5*R + 6 + R = 114      Combine like terms on the left

6R + 6 = 114              Subtract 6 from both sides.

6R +6-6 = 114-6        Combine

6R = 108                   Divide by 6

6R/6 = 108/6

R = 18

P+R = 114

P + 18 = 104              Subtract 18 from both sides.

P + 18-18=104 -18     Do the subtraction

P = 86

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