Question 252604
# 1


Let s = # of senior tickets and j = # of junior tickets



Since there are 35 tickets in total, and we're assuming that only junior and senior tickets are sold, this means that {{{j+s=35}}}. In other words, adding up the two totals will give you the grand total of 35.



Also, because "The number of tickets sold to seniors must be four times the number of tickets sold to juniors", we know that {{{s=4j}}}. In English, the number of senior tickets 's' is 4 times the number of junior tickets 'j'.



{{{j+s=35}}} Start with the first equation.



{{{j+4j=35}}} Plug in {{{s=4j}}}



{{{5j=35}}} Combine like terms on the left side.



{{{j=(35)/(5)}}} Divide both sides by {{{5}}} to isolate {{{j}}}.



{{{j=7}}} Reduce.



So there are 7 junior tickets.



{{{s=4j}}} Go back to the second equation



{{{s=4*7}}} Plug in {{{j=7}}}



{{{s=28}}} Multiply



So there are 28 senior tickets.



As a check, take note that 28 is indeed 4 times 7 AND 28+7=35. So we've met our conditions.


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# 2


Let t = cost of diamond today and y = cost of diamond last year



Since "A diamond today costs 10$ more than twice what it cost last year", we can say that {{{t=2y+10}}} (ie double the cost from last year 'y' and add 10 to get the new cost today 't').



Also, because "The sum of the cost (last year and this year) is 2500$", we know that {{{t+y=2500}}} (just add up the two individual costs to get the grand total of $2500)



{{{t+y=2500}}} Start with the second equation.



{{{2y+10+y=2500}}} Plug in {{{t=2y+10}}}



{{{3y+10=2500}}} Combine like terms on the left side.



{{{3y=2500-10}}} Subtract {{{10}}} from both sides.



{{{3y=2490}}} Combine like terms on the right side.



{{{y=(2490)/(3)}}} Divide both sides by {{{3}}} to isolate {{{y}}}.



{{{y=830}}} Reduce.



So the cost of the diamond last year was $830.



If you want to keep going then...



{{{t=2y+10}}} Go back to the first equation



{{{t=2(830)+10}}} Plug in {{{y=830}}}



{{{t=1660+10}}} Multiply



{{{t=1670}}} Add



So the cost of the diamond today is $1670.