Question

Timmy has some red marbles, some blue marbles, and some yellow marbles; he has 100 marbles in total. He has 4 times as many red marbles as blue marbles, and 5 times as many yellow marbles as red marbles. Determine how many marbles of each color Timmy has. How many red marbles does Timmy have? How many blue marbles does he have? How many yellow marbles does he have?

Answer 1

Timmy has 4 blue marbles, 16 red marbles, and 80 yellow marbles. This is determined by setting up an algebraic equation based on the given relationships between the quantities of each color and solving for the number of blue marbles.

Step-by-step explanation:

To solve for the number of red, blue, and yellow marbles Timmy has, let's define variables for the number of each color marble:

• Let b be the number of blue marbles.
• Timmy has 4 times as many red marbles as blue marbles, so let 4b be the number of red marbles.
• Timmy has 5 times as many yellow marbles as red marbles, so let 5(4b) = 20b be the number of yellow marbles.

The total number of marbles is 100, so we have the equation: b + 4b + 20b = 100.

Combining like terms, we get: 25b = 100.

Dividing both sides by 25 gives us: b = 4.

Therefore, Timmy has:

• 4 blue marbles (since b = 4),
• 16 red marbles (since 4b = 4*4), and
• 80 yellow marbles (since 20b = 20*4).