Question

To win q game, Nicholas needs to collect as many coloured beads as possible. Each colour would be awarded a certain number of points as shown below:

Red: 5 points
Yellow: 3 points
Red: 1 point.

The ratio of the number of RED beads to the number of YELLOW beads to the number of GREEN beads collected was 3:2:5. Nicholas has 208 points. How many beads did he collect altogether?​

Answer 1

Explanation:

Let's call the number of red beads collected 3x, the number of yellow beads collected 2x, and the number of green beads collected 5x. Then we can write an equation to express the total number of points:

Total points = 5*(3x) + 3*(2x) + 1*(5x) = 15x + 6x + 5x = 26x

We are told that the total number of points collected is 208, so we can set this equal to our expression for the total number of points and solve for x:

26x = 208

x = 8

Now we can find the number of each color of bead collected:

Number of red beads = 3x = 24

Number of yellow beads = 2x = 16

Number of green beads = 5x = 40

And the total number of beads collected is:

24 + 16 + 40 = 80

Therefore, Nicholas collected 80 beads altogether.

Answer 2

Nicholas collected a total of 80 beads.

Explanation:

The given ratio of collected beads is:

• Red : Yellow : Green = 3 : 2 : 5

So for every 3 red beads collected, Nicholas collected 2 yellow beads and 5 green beads.

Therefore, the total number of beads collected can be written as:

• 
  `3x + 2x + 5x` (where x is a constant to be found).

If each red bead is worth 5 points, each yellow bead is worth 3 points, each green bead is worth 1 point, and the total points are 208 then:

`\implies (5 \cdot 3x) + (3 \cdot 2x) + (1 \cdot 5x) = 208`

To find the value of x, solve the equation:

`\implies 15x + 6x + 5x = 208`

`\implies 26x = 208`

`\implies x = 8`

To calculate the total number of beads Nicholas collected, substitute the found value of x into the equation for the total number of beads:

`\begin{aligned}\implies \textsf{Total number of beads}&=3x + 2x + 5x\\&= 10x\\&= 10 \cdot 8\\&= 80\end{aligned}`

Therefore, the total number of beads Nicholas collected was 80:

• 24 red beads
• 16 yellow beads
• 40 green beads