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| 1. |
match tickets for 4 adults and 7 childrens costs a total of €45 adult tickets costs twice the price of childs ticket a) write an equation for the cost of the tickets b) work out the cost of an adult ticket |
| Answer» <html><body><p>-step explanation:Five hundred tickets were sold for a certain music concert. The tickets for the adults and children sold for $7.50 and $4.00, respectively, and the <a href="https://interviewquestions.tuteehub.com/tag/total-711110" style="font-weight:bold;" target="_blank" title="Click to know more about TOTAL">TOTAL</a> receipts for the performance were $3,312.50. How many of each kind of ticket were sold?Answer: <a href="https://interviewquestions.tuteehub.com/tag/375-309985" style="font-weight:bold;" target="_blank" title="Click to know more about 375">375</a> adult tickets were sold and 125 children tickets were sold.Solutions:Essentially you have two sentences: <a href="https://interviewquestions.tuteehub.com/tag/one-585732" style="font-weight:bold;" target="_blank" title="Click to know more about ONE">ONE</a> sentence deals with the total amount of tickets and the other sentence deals with how much money was <a href="https://interviewquestions.tuteehub.com/tag/paid-1145567" style="font-weight:bold;" target="_blank" title="Click to know more about PAID">PAID</a> for the tickets.One sentence could be rewritten as ''the total amount adult tickets'' plus ''the total amount of children tickets'' equals 500 tickets. The second sentence could be rewritten as ''the amount of adult tickets'' times $7.50 plus ''the amount of children tickets'' times $4.00 equals $3,312.50Let's rewrite the sentences again.Sentence (1): ''the total amount adult tickets'' + ''the total amount of children tickets'' = 500Sentence (2): $\$7.50\times \ $''the total amount adult tickets'' + $%\$4.00\times \ $''the total amount of children tickets'' = 3It is going to become tiresome writing the phrases ''the total amount adult tickets'' and ''the total amount of children tickets'' over and over. Therefore, let the symbol x represent the phrase ''the total amount adult tickets'', and let the symbol y represent the phrase ''the total amount of children tickets''\begin{eqnarray*}&& \\(1) &:&x+y=500 \\&& \\(2) &:&\$7.50x+\$4.00y=\$3,312.50 \\&& \\&&\end{eqnarray*}We have converted a <a href="https://interviewquestions.tuteehub.com/tag/narrative-1110720" style="font-weight:bold;" target="_blank" title="Click to know more about NARRATIVE">NARRATIVE</a> statement of the problem to an equivalent algebraic statement of the problem</p></body></html> | |