. If ON = 4x – 6, LM = 3x + 5, NM = x – 4, and OL = 4y – 3, find the values of x and y for which LMNO must be a parallelogram.
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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