Answered

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6. A cookie jar contains 315 M&M's. There are only brown and
green M&M's in
the jar. The number of green M&M's is 8 times that of the brown M&M's.
Write and solve a system to find out how many of each color M&M are in the
jar. (Remember: You have to WRITE AND SOLVE a system. No credit for
guess and check.)

Sagot :

Answer:

280 Green and 35 Brown

Step-by-step explanation:

To find out how many green and brown m&ms are in the jar you have to attempt to guess until you get a number that adds up to 315 (I'm sure there is a better way but I don't remember much high school math.) You can tell that there are more green m&ms than brown because it is being multiplied by the brown. However, there is one way to get a somewhat close estimate of the number. If you divide 315 and eight you get 39. It is not exact but it is close. Since there are only two m&m types, you only need to subtract them by a little bit. That is how i assumed to try the number 35

Eight and 35

Eight times 35 is 280 so it is perfect because when you add 280 and 35  you get 315.

Therefore, there are 280 green m&ms and 35 brown.

I hope this is detailed enough to help you understand how to solve these types of equations.

batolisis

The system of equations representing the problem is

[tex]b+g=315\\8b-g=0[/tex]

and we have [tex]35[/tex] brown M&M's and [tex]280[/tex] green M&M's in the cookie jar.

Formulating the equations

If we let [tex]b[/tex] represent the number of brown M&M's and [tex]g[/tex] the number of green M&M's, then, from the sentence

"...A cookie jar contains 315 M&M's. There are only brown and green M&M's in the jar..."

we can construct the algebraic equation

[tex]b+g=315[/tex]

Also, from the sentence

"...The number of green M&M's is 8 times that of the brown M&M's..."

we can construct the algebraic equation

[tex]g=8b\implies 8b-g=0[/tex]

overall, we have the system of equations with unknowns [tex]b[/tex] and [tex]g[/tex]

[tex]b+g=315\\8b-g=0[/tex]

Solving the system of equations

Adding the two equations, we get

[tex](b + 8b) +(g + (-g))=315+0\\9b=315\\\\\dfrac{9b}{9}=\dfrac{315}{9}\\\\b=35[/tex]

Substituting this value for [tex]b[/tex] into the relationship [tex]g=8b[/tex]

[tex]g=8b\\g=8(35)=280[/tex]

Therefore, we have [tex]35[/tex] brown M&M's and [tex]280[/tex] green M&M's

Learn more about word problems and systems of equations here https://brainly.com/question/14111058

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