Q4. - Algebra 1

Question

Drew has $50$ red, green, and blue marbles. He has six more red marbles than blue marbles and four fewer green marbles than blue marbles. Write and solve an equation to determine how many blue marbles Drew has.

Step-by-Step Solution

Answer

Drew has number of the blue marbles is $16$.

Step 1. Given information.

Drew has $50$ red, green and blue marbles.

He has $6$ more red marbles than blue marbles.

He has $4$ lesser green marbles than blue marbles.

Step 2. To find the expression of the problem.

Suppose the number of blue marbles is $=a$.

Therefore, the number of red marbles is $=a+6$.

And, the number of green marbles is $=a–4$.

According to the question:

$\left(a+6\right)+\left(a-4\right)+a=50$

Therefore, the expression of the question is $\left(a+6\right)+\left(a-4\right)+a=50$.

Step 3. To find the value of the a.

$\begin{array}{l}\left(a+6\right)+\left(a-4\right)+a=50\\ \Rightarrow 6+a+a-4+a=50\\ \Rightarrow 3a+2=50\\ \Rightarrow 3a=48\\ \Rightarrow a=\frac{48}{3}\\ \Rightarrow a=16\end{array}$

Hence, Drew has number of the blue marbles is $16$.