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Ronch [10]
3 years ago
10

Tina is saving to buy a notebook computer. She has two options. The first option is to put $200 away initially and save $10 ever

y month. The second option is to put $100 away initially and save $30 every month. After how many months would Tina save the same amount using either options? How much would she save with either option?
Mathematics
1 answer:
Mamont248 [21]3 years ago
7 0

Answer: In five months,she will save the same money which is $250.

Step-by-step explanation:

Using the first statement we can generate the function y=10x + 200  and using the second statement we can also generate the function y = 30x + 100 . Now using the two equations solve for x and y to determine how many months they cost the same.

y = 10x + 200

y = 30x + 100  

Substitute the value of x in the first equation into the second equation.

30x + 100= 10x + 200   now solve for x

         -100            -100

30x = 10x + 100

-10x    -10x

20x = 100

x= 5  

This means in five months Tina will save the same amount. Now to find out how much the amount is, plot the value of x into one of the equations and solve for  y.

y = 10(5) + 200

y = 50 + 200

y = 250  

She will save $250 with either option.

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Which equations have the same slope as the graph above? Select all that apply.
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Given:

The graph given passes through two points (0, 2) and (-4, 8).

General Idea:

We can find the slope (m) of a line passing through two points say A and B using the below formula.

A(x_1,y_1) \; and \; B(x_2,y_2) \; the\; two\; points\\ \\ Slope\; (m)\; =\;   \frac{y_2-y_1}{x_2-x_1}

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Out of the five options given , we need to check which options have slope as -6/4 or -3/2 by rewriting (if needed) the given to slope intercept form y =mx + b and compare the same.

Conclusion:

Rewriting the first option, the slope is -6/4 as shown below.

y=\frac{12-6x}{4}=\frac{12}{4} -\frac{6x}{4}  =-\frac{6}{4}x+3

Rewriting the fourth option, the slope is -3/2 as show below.

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Divide by 2 throughout the equation

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