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vivado [14]
2 years ago
9

A movie theater charges 8 dollars for adults and 4 dollars for seniors. On a particular day when 353 people paid an admission, t

he total receipts were 1688 dollars
Mathematics
1 answer:
sammy [17]2 years ago
7 0

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

a \times 8 + s \times 4 = 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

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