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hram777 [196]
3 years ago
10

Ms. Thornton is buying treats for her top 10 algebra students in each of her two classes (20 treats total). She’s only willing t

o spend $30 and finds individualized candy packs for $1.75 each. What is the maximum number of packs that she will be able to buy? Will that be enough for all of her students?
Mathematics
1 answer:
Paladinen [302]3 years ago
5 0

Answer:

Mrs Thornton can buy almost 17 candy packs if she has $30 to spend and one pack cost $1.75.

No, it will not be enough because total students are 20 and total candy packs that can be bought are 17.

Step-by-step explanation:

Total treats to buy = 20

Total cost to spend = $30

Price of one candy pack = 1.75

We need to find:

a) What is the maximum number of packs that she will be able to buy?

Price of 1 candy pack = $1.75

If she spends $30, divide 30 by 1.75 to get the number of candy packs she can buy

Number of candy packs = \frac{30}{1.75} = 17.14 \approx 17

So, Mrs Thornton can buy almost 17 candy packs if she has $30 to spend and one pack cost $1.75

b)  Will that be enough for all of her students?

No, it will not be enough because total students are 20 and total candy packs that can be bought are 17.

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Answer:

The answer is below

Step-by-step explanation:

A) i)

For Anna initially, she has $0 from making 0 envelopes. After making 400 envelopes she has $20. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (400, 20). Using the equation of a line:

y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{20-0}{400-0}(x-0)\\\\y=\frac{1}{20} x

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For Jason initially, he has $0 from making 0 envelopes. For every 250 envelopes he has $10. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (250, 10). Using the equation of a line:

y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{10-0}{250-0}(x-0)\\\\y=\frac{1}{25} x

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x:   200     400       600     800     1000

y:    8         16           24        32       40

The graph is plotted using geogebra online graphing

b) From the table above we can see that Anna makes more stuffing than Jason.

c) Anna has a savings of $100. Hence this can be represented by the points (0, 100) and (250, 10). Using the equation of a line:

y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-100=\frac{20-0}{400-100}(x-0)\\\\y=\frac{1}{15} x+100

We can see from the graph that there is a y intercept at 100. That is the earnings starts from 100.

The equation of a line is given as y = mx + b, where m is the slope and b is the y intercept (initial value)

For the first graph, the slope is 1/20 and the initial value is 0 while for the second graph the slope is 1/15 and the initial value is 100

D) The line pass through (10, 10) and (100, 40), hence:

y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-10=\frac{40-10}{100-10}(x-10)\\\\y-10=\frac{1}{3} (x-10)\\\\y=\frac{1}{3}x+\frac{20}{3}

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