Amy has $30 to spend on snacks and beverages for herself and her friends at the movie theater. The cost for nachos was $5. The c
ost for each beverage was half the cost of the nachos.
(a) Sketch a graph that represents this situation and label the intercepts. Use one axis to represent the number nachos and the other axis to represent the number of beverages.
(b)Explain your graph.
(a) Sketch a graph that represents this situation and label the intercepts. Use one axis to represent the number nachos and the other axis to represent the number of beverages.
(b)Explain your graph.
1 answer:
Amy has $30 to spend on snacks and beverages for herself and her friends at the movie theater. The cost for nachos was $5. The cost for each beverage was half the cost of the nachos
Let x be the number of nachos and y be the number of beverages
The cost for nachos was $5. So the cost of 'x' nachos = 5x
The cost for each beverage was half the cost of the nachos.
The cost of each beverage =
so the cost of y beverage = 2.5 y
Cost of x nachos + cost of y beverage = total amount spend
5x + 2.5y = 30
Now we find x and y intercept
When Amy does not buy any beverages we put y=0
5x + 2.5(0) = 30
5x = 30
x= 6. The x intercept is (6,0)
When Amy does not buy any nachos we put x=0
5(0) + 2.5y = 30
2.5y = 30
y=12. The y intercept is (0,12)
The graph is attached below
(b) The graph is a straight line. From the graph we can see that when Amy does not buy any nachos then she can spend #30 to buy 12 beverages .
when Amy does not buy any beverages then she can spend #30 to buy 6 nachos.
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- If is *directly* proportional to
, then we mean that as
changes,
changes in the same direction. In other words, if
is in/decreased, then
also in/decreases. The rate of in/decrease doesn't have to be one-to-one; for example, we could have
increase by 1 unit while
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- On the other hand, if is *inversely* proportional to
, then a change in
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that goes in the opposite direction. A common example involves taking a rectangle of constant area and adjusting the width
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and
, or
and
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is satisfied.
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On to your exercises:
(1a) Looks like stands for number of apples. Then we're told that the cost
, which means that for every apple, the cost increases by 2.3 dollars. So the constant of proportionality is 2.3. In the language of proportionality, we could then say that the cost of apples is directly proportional to the number of apples by a factor of 2.3.
(1b) 5.4
(1c) 12.5