Alex is buying a sweater that originally costs $35 and a pair of jeans that originally cost $28. If the sweater is marked down 3
2 answers:
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Answer:
Step-by-step explanation:
See the figure below.
This is how you graph directly from the equation in the slope-intercept form (y = mx + b) without having to create a table of x and y values.
The equation is
y = -2/3 x + 1
Compare it with
y = mx + b
b = 1
The y-intercept is 1, so mark 1 on the y-axis. (You already did.)
I placed a black dot there.
The slope is m.
m = -2/3
slope = m = rise/run
A slope of -2/3 can be though of as -2 rise and 3 run. That means start from the y-intercept, and go -2 in y (a rise of 2 down) and 3 in x (a run 3 right). Point graphed in red.
Mathematically, -2/3 is the same as 2/(-3), so starting again from the y-intercept, this slope can also be though of as rise of 2 in y (a rise of 2 up) and a run of -3 in x (a run of 3 left). Point graphed in green.
The line is graphed in blue.
A movie theater charges 8 dollars for adults and 4 dollars for seniors. On a particular day when 353 people paid an admission, the total receipts were 1688 dollars. How many who paid were adults? . How many who paid were seniors?
<em><u>Answer:</u></em>
There were 69 adults and 284 seniors
<em><u>Solution:</u></em>
Let "a" be the number of adults
Let "s" be the number of seniors
Cost of 1 adult = $ 8
Cost of 1 senior = $ 4
<em><u>On a particular day when 353 people paid an admission</u></em>
Therefore,
number of adults + number of seniors = 353
a + s = 353
a = 353 - s ---------- eqn 1
<em><u>The total receipts were 1688 dollars</u></em>
Therefore, we frame a equation as:
number of adults x Cost of 1 adult + number of seniors x Cost of 1 senior = 1688
8a + 4s = 1688 ---------- eqn 2
<em><u>Let us solve eqn 1 and eqn 2</u></em>
<em><u>Substitute eqn 1 in eqn 2</u></em>
8(353 - s) + 4s = 1688
2824 -8s + 4s = 1688
4s = 2824 - 1688
4s = 1136
<h3>s = 284</h3><em><u>Substitute s = 284 in eqn 1</u></em>
a = 353 - 284
<h3>a = 69</h3>Thus there were 69 adults and 284 seniors in movie theater