Math / Algebra

QuestionEmily is making purple frosting to decorate cupcakes for her birthday party. She adds 8 drops of red food coloring to a bowl of white frosting. Emily wants the frosting to be a pinkish shade of purple, so she adds less blue food coloring than red food coloring.
Let $b$ represent the number of drops of blue food coloring that Emily might add. Which inequality models the story? $b>8$ $b \geq 8$ $b<8$ $b \leq 8$
Graph the inequality that models the story. To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it. Submit Work it out

Studdy Solution

STEP 1

What is this asking? How many drops of blue food coloring can Emily add to have less blue than red, and how do we show that on a number line? Watch out! Don't mix up the greater than and less than signs!
We want less blue than red.

STEP 2

1. Write the Inequality
2. Graph the Inequality

STEP 3

Alright, so Emily is mixing up some awesome purple frosting!
She's already put in $\text{8}$ drops of red.
She wants less blue than red.

STEP 4

We know that $b$ is the number of drops of blue food coloring.
Since $b$ has to be less than the number of drops of red, and there are $\text{8}$ drops of red, we can write this as $b < 8$ .
That's it! $b < 8$ means that $b$ can be any number smaller than $\text{8}$ .

STEP 5

Now, let's graph this bad boy on a number line!
We'll start by drawing a number line with $\text{8}$ clearly marked.

STEP 6

Since our inequality is $b < 8$ , we're looking for all the numbers that are less than $\text{8}$ .
This means we don't include $\text{8}$ itself.
To show this on the graph, we'll use an open circle at $\text{8}$ .
An open circle means we get really close to $\text{8}$ , but we don't actually touch it!

STEP 7

Now, since we want all the numbers less than $\text{8}$ , we'll draw an arrow pointing to the left from the open circle at $\text{8}$ .
This arrow represents all the numbers smaller than $\text{8}$ , going all the way to negative infinity!

STEP 8

The inequality that models the story is $b < 8$ .
The graph should have an open circle at $\text{8}$ with an arrow pointing to the left.

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Studdy Solution

STEP 1

What is this asking? How many drops of blue food coloring can Emily add to have less blue than red, and how do we show that on a number line? Watch out! Don't mix up the greater than and less than signs!
We want less blue than red.

STEP 2

1. Write the Inequality
2. Graph the Inequality

STEP 3

Alright, so Emily is mixing up some awesome purple frosting!
She's already put in $\text{8}$ drops of red.
She wants less blue than red.

STEP 4

We know that $b$ is the number of drops of blue food coloring.
Since $b$ has to be less than the number of drops of red, and there are $\text{8}$ drops of red, we can write this as $b < 8$ .
That's it! $b < 8$ means that $b$ can be any number smaller than $\text{8}$ .

STEP 5

Now, let's graph this bad boy on a number line!
We'll start by drawing a number line with $\text{8}$ clearly marked.

STEP 6

STEP 7

Now, since we want all the numbers less than $\text{8}$ , we'll draw an arrow pointing to the left from the open circle at $\text{8}$ .
This arrow represents all the numbers smaller than $\text{8}$ , going all the way to negative infinity!

STEP 8

The inequality that models the story is $b < 8$ .
The graph should have an open circle at $\text{8}$ with an arrow pointing to the left.

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Studdy Solution

STEP 1

What is this asking? How many drops of blue food coloring can Emily add to have *less* blue than red, and how do we show that on a number line? Watch out! Don't mix up the greater than and less than signs!We want *less* blue than red.

STEP 2

1. Write the Inequality2. Graph the Inequality

STEP 3

Alright, so Emily is mixing up some *awesome* purple frosting!She's already put in 8\text{8}8 drops of red.She wants *less* blue than red.

STEP 4

We know that bbb is the number of drops of blue food coloring.Since bbb has to be *less than* the number of drops of red, and there are 8\text{8}8 drops of red, we can write this as b<8b < 8b<8.That's it! b<8b < 8b<8 means that bbb can be any number smaller than 8\text{8}8.

STEP 5

Now, let's **graph** this bad boy on a number line!We'll start by drawing a number line with 8\text{8}8 clearly marked.

STEP 6

STEP 7

Now, since we want all the numbers *less than* 8\text{8}8, we'll draw an arrow pointing to the *left* from the open circle at 8\text{8}8.This arrow represents *all* the numbers smaller than 8\text{8}8, going all the way to negative infinity!

STEP 8

The inequality that models the story is b<8b < 8b<8.The graph should have an open circle at 8\text{8}8 with an arrow pointing to the left.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? How many drops of blue food coloring can Emily add to have less blue than red, and how do we show that on a number line? Watch out! Don't mix up the greater than and less than signs!
We want less blue than red.

1. Write the Inequality
2. Graph the Inequality

Alright, so Emily is mixing up some awesome purple frosting!
She's already put in $\text{8}$ drops of red.
She wants less blue than red.

We know that $b$ is the number of drops of blue food coloring.
Since $b$ has to be less than the number of drops of red, and there are $\text{8}$ drops of red, we can write this as $b < 8$ .
That's it! $b < 8$ means that $b$ can be any number smaller than $\text{8}$ .

Now, let's graph this bad boy on a number line!
We'll start by drawing a number line with $\text{8}$ clearly marked.

Now, since we want all the numbers less than $\text{8}$ , we'll draw an arrow pointing to the left from the open circle at $\text{8}$ .
This arrow represents all the numbers smaller than $\text{8}$ , going all the way to negative infinity!

The inequality that models the story is $b < 8$ .
The graph should have an open circle at $\text{8}$ with an arrow pointing to the left.