Question

8th grade math plz help!

Bottles of water sell for $1.50 each.

Graph the relationship between the number of bottles of water sold and the total cost.

Bottles Sold Total Cost



In a salsa recipe, the number of tomatoes added is proportional to the amount of salt added. This graph shows the relationship.



What is the unit rate for the number of tomatoes to the tsp of salt?




Relationship B has a greater rate than Relationship A. This graph represents Relationship A.

Which equations could represent Relationship B?

Select each correct answer.


y=2/3x

y=1/4x

y = 0.6x

y=3/4x


Relationship A has a greater rate than Relationship B. This table represents Relationship B.

Hours worked 2 4 5 8
Amount paid ($) 25 50 62.50 100
Which equation could represent Relationship A?

Hours worked is represented by x and Amount paid is represented by y.

Select each correct answer.


y = 11.5x

y = 12.25x

y = 13x

y = 12.75x



The equation y = 14x represents the number of pages Printer A can print over time, where y is the number of pages and x is time in minutes. This table shows the number of pages Printer B can print over time.

How many pages does each printer print per minute, and which printer prints at a faster rate?

Printer B
Time (min) Pages Printed
3 48
5 80
8 128
12 192

Answer 1

QUESTION 1

The price of a bottle of water is $1.50 dollars

If
`x` units are sold, the total cost is
`1.50x`

We can write the total cost as a function of the unit price.

`C(x)=1.5x`

To graph this function we can choose at least two points.

`\left\begin{array}{ccc}Bottles\:sold&|&Total\:Cost\\0&|&0\\1&|&1.5\\2&|&3\end{array}\right`

We now plot these points and use it to draw our graph. See attachment.

QUESTION

At a point on the graph we can determine that, for every 6 amount of salt added, 18 amount of tomatoes is also added.

So the unit rate of the number of tomatoes to the number of salt added is

`(18)/(6)`

We express the denominator as one to get the unit rate, so we divide both the numerator and denominator by 3.

`(3)/(1)`

Therefore the unit rate of tomatoes to salt is 3:1 or simply 3.

QUESTION 3

We calculate the rate of relationship B and compare to the rate of the given options,

The graph passes through,

`(8,4)`

and

`(4,2)`

So the rate of this graph is the same as the slope,

`Rate\:of\:A=(4-2)/(8-4) =(2)/(4) =(1)/(2)`

The rate of B is greater than
`(1)/(2)`. So we select all the relationships that has a slope greater than
`(1)/(2)`.

These are;

`y=(2)/(3)x`,
`y=0.6x` and
`y=(3)/(4)x`

QUESTION 4

We again find the rate of relationship B and compare it to the rates in the given options. We choose any two points from the table and use it to find the rate of B.

Let us use,

`(2,25)` and
`(4,50)`

`Rate\:of\:B=(50-25)/(4-2) =(25)/(2)=12.5`

Since relationship A is greater, we choose all the relationship that has a slope more than 12.5.

These are,

`y=13x` and
`y=12.75x`

QUESTION 5

Again we find the rate of printer B and compare it to printer A.

Let us use the points,
`(3,48)` and
`(5,80)`

`Rate\:of\:Printer\:B=(80-48)/(5-3) =(32)/(2)=16`

Hence Printer A prints 14 words per minute, while printer B prints 16 words per minute.

Therefore printer B prints faster than printer A.