Question

Ivan has 6 times as many blue beads as red beads. he has 49 red and blue beads in all. how many blue beads does Ivan have

Answer 1

The total number of blue beads with Ivan is $\boxed{\bf 42}$.

Further explanation:

It is given that Ivan has $6$ times as many blue beads as red beads.

The total number of beads are $49$.

Calculation:

Assume the beads of red color are denoted by $R$ and the beads of blue color are denoted by $B$.

Now, given that there are total $49$ beads and this can be written in the form of an equation as follows:

$\boxed{R+B=49}$     ......(1)

Also, given that Ivan has $6$ times as many blue beads as red beads and this can written as follows:

$\boxed{6R=B}$         ......(2)

Substitute the value $6R=B$ in equation (1), we get

$\begin{aligned}R+6R&=49\\7R&=49\\R&=\dfrac{49}{7}\\R&=7\end{aligned}$

Therefore, Ivan has $7$ red beads.

Substitute $R=7$ in equation (1).

$\begin{aligned}B&=6\cdot 7\\&=42\end{aligned}$

This implies that number of blue beads are $42$.

Thus, the total number of blue beads with Ivan is $\boxed{\bf 42}$.

Learn more

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Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Linear equations in two variables

Keywords: Linear equations in one variable, linear equations in two variables, substitution, elimination, function, sets, real numbers, ordinates, abscissa, interval.

Answer 2

Let

x--------> the number of blue beads

y--------> the number of red beads

we know that

$x+y=49$

$x=49-y$ -------> equation $1$

$x=6y$ ------> equation $2$

equate equation $1$ and equation $2$

$49-y=6y\\ 6y+y=49\\ 7y=49\\\\ y=\frac{49}{7} \\ \\ y=7$

find the value of x

$x=6*7\\ x=42$

therefore

the answer is

Ivan has $42$ $blue beads$