Answered

Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

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].

Learn more

1. Problem on the equation of the circle https://brainly.com/question/1952668

2. Problem on the center and radius of an equation https://brainly.com/question/9510228

3. Problem on the general form of the equation of the circle https://brainly.com/question/1506955

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.