Question

I will attach a picture to this question so you can understand it better.

Answer 1

Here are the given information:

1. 7 red beads for every 4 blue beads

2. total of 44 beads (red and blue)

Find: the number of red beads

Solution:

We can solve this in two ways. We can solve this using proportion or we can solve this by counting.

Let's start counting first. Let's say 7 red beads and 4 blue beads is 1 set. So, for every set, we already have 7 + 4 = 11 beads in total.

First set = 7 red bead + 4 blue beads = 11 beads

Second set = 7 red bead + 4 blue beads = 11 beads

Third set = 7 red bead + 4 blue beads = 11 beads

Fourth set = 7 red bead + 4 blue beads = 11 beads

If we add all the 4 sets, we have a total of 44 beads. If we add all the RED beads only, we get 7 red beads x 4 sets = 28 red beads.

Therefore, Lily used 28 red beads.

Now, using proportion, we can have this equation:

`\frac{7\text{red beads}}{4\text{blue bead}}=\frac{x\text{ red beads}}{(44-x\text{ red)blue beads}}`

where x = the total number of red beads and we got 44 - x as the number of blue beads.

The next thing that we need to do here is to solve for x.

1. To solve for x, do cross multiplication first.

`7(44-x)=4x`

2. Multiply 7 to the numbers inside the parenthesis.

`308-7x=4x`

3. Add 7x on both sides of the equation.

`\begin{gathered} 308-7x+7x=4x+7x \\ 308=11x \end{gathered}`

4. Lastly, divide both sides by 11.

`\begin{gathered} (308)/(11)=(11x)/(11) \\ 28=x \end{gathered}`

As we can see, the value of x = 28. Lily used 28 red beads.