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

Sagot :

Let

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

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

we know that

[tex] x+y=49 [/tex]

[tex] x=49-y [/tex] -------> equation [tex] 1 [/tex]

[tex] x=6y [/tex] ------> equation [tex] 2 [/tex]

equate equation [tex] 1 [/tex] and equation [tex] 2 [/tex]

[tex] 49-y=6y\\ 6y+y=49\\ 7y=49\\\\ y=\frac{49}{7} \\ \\ y=7 [/tex]

find the value of x

[tex] x=6*7\\ x=42 [/tex]

therefore

the answer is

Ivan has [tex] 42 [/tex] [tex] blue beads [/tex]

The total number of blue beads with Ivan is [tex]\boxed{\bf 42}[/tex].

Further explanation:

It is given that Ivan has [tex]6[/tex] times as many blue beads as red beads.

The total number of beads are [tex]49[/tex].

Calculation:

Assume the beads of red color are denoted by [tex]R[/tex] and the beads of blue color are denoted by [tex]B[/tex].

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

[tex]\boxed{R+B=49}[/tex]     ......(1)

Also, given that Ivan has [tex]6[/tex] times as many blue beads as red beads and this can written as follows:

[tex]\boxed{6R=B}[/tex]         ......(2)

Substitute the value [tex]6R=B[/tex] in equation (1), we get

[tex]\begin{aligned}R+6R&=49\\7R&=49\\R&=\dfrac{49}{7}\\R&=7\end{aligned}[/tex]

Therefore, Ivan has [tex]7[/tex] red beads.

Substitute [tex]R=7[/tex] in equation (1).

[tex]\begin{aligned}B&=6\cdot 7\\&=42\end{aligned}[/tex]

This implies that number of blue beads are [tex]42[/tex].

Thus, the total number of blue beads with Ivan is [tex]\boxed{\bf 42}[/tex].

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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.