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gizmo_the_mogwai [7]
3 years ago
9

Use your knowledge of the process of "Writing an equation given two points" to solve the following problem: A vendor has learned

that, by pricing his deep fried bananas on a stick at $1.00, sales will reach 100 per day. Raising the price to $2.00 will cause the sales to fall to 52 per day. Let y be the number of the vendor sells at x dollars each. Write a linear equation that models the number of sold per day when the price is x dollars each.
Mathematics
1 answer:
nydimaria [60]3 years ago
3 0

Answer: Our required linear equation would be x+48y=148

Step-by-step explanation:

Since we have given that

Cost of deep fried bananas on a stick = $1.00

Number of sales reached = 100 per day

Cost of deep fried bananas on a stick becomes = $2.00

Number of sales reached = 52 per day.

Let x is the number of dollars each.

Let y be the number of vendors sale.

So, we need to form the linear equation:

As we know the formula for two point slope form:

y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-1=\dfrac{2-1}{52-100}(x-100)\\\\y-1=\dfrac{1}{-48}(x-100)\\\\-48(y-1)=(x-100)\\\\-48y+48=x-100\\\\-48y=x-100-48\\\\-48y=x-148\\\\x+48y=148

Hence, our required linear equation would be x+48y=148

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Sara sells homemade blueberry jelly (b) and strawberry jam (s) at the farmer's market. It is the end of berry picking season, so
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System of inequalities representing given scenario is as follows

x + y ≤40  

5x + 4y ≥ 120    

<h3><u>Solution:</u></h3>

Given that Sara sells homemade blueberry jelly (b) and strawberry jam (s) at the farmer's market. She has enough berries for no more than 40 jars.

The blueberry jelly sells for $5 per jar,  

And the strawberry jam sells for $4 per jar.

Sara's goal is to make at least $120

Need to write system of inequalities for above scenario.

Let’s assume number of jars of blueberry jelly be represented by variable “x”

And assume number of jars of strawberry jam be represented by variable “y”

<em><u>Let’s create first inequality  </u></em>

As it is given that Sara has enough berries for no more than 40 jars, so total number of jars cannot be more than 40.  

=> Number jars of blueberry jelly + number of jars of strawberry jam ≤40

=>  x + y ≤ 40 ------(1)

<em><u>Now let’s create second inequality </u></em>

Selling Price of 1 blueberry jelly = $5  

So Selling Price of "x" blueberry jelly =x \times 5=5 x

Selling Price of 1 strawberry jam = $4

So Selling Price of "y" strawberry jam = \$ 4 \times \mathrm{y}=4 y

So amount generated by selling x blueberry jelly and y strawberry jam = 5x + 4y

And as Sara’s goal is to generate at least $120, so amount generated by selling “x” blueberry jelly and “y” strawberry jam must be greater than $120  

=> 5x + 4y ≥ 120   ------ (2)

Hence system of inequalities representing given scenario is as follows :

x + y ≤40  

5x + 4y ≥ 120    

3 0
3 years ago
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