Step-by-step explanation: Â Now, the main unknown here is "the # of adult tickets." Â Another thing that's unknown is the "the # of children's tickets." Â So, we will assign 2 variables as follows:
Let a = # of adult tickets
and c = # of children's tickets.
The next step is to set up the equations out of the unknowns that follow the word problem. Â Here they are as follows:
a adult tickets + c children's tickets = 460 tickets altogether, so
a + c = 460.
Now, since we know how much all the tickets cost altogether, $3143, here comes the next equation:
(($8.75/adult ticket) * a adult tickets) + (($3.50/children's ticket) * c children's tickets) = $3143, so
8.75a + 3.50c = 3143 since the units, adult tickets and children's tickets, cancel each other out.
Now, since we are looking for the # of adult tickets, we can express the simple equation, a + c = 460, as c in terms of a:
a + c  = 460
-a    = -a     (i.e. -a on each side of the equation to eliminate a on the left side.)
       Â
c = 460 - a
Now that we have the equation c in terms of a, we can plug it into the other equation, 8.75a + 3.50c = 3143. Â Here it is as follows:
8.75a + 3.50 * (460-a) = 3143 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â substitute method
8.75a + [(3.50 * 460) - (3.50 * a)] = 3143 Â Â Â Â Â Â distributive property
8.75a + (1610 - 3.50a) = 3143 Â Â Â I multiplied the two terms in parentheses inside the brackets.
8.75a + 1610 - 3.50a = 3143 Â Â Â Â Â Everything's out of the parentheses.
5.25a + 1610 = 3143 Â Â Â Â Â Â Â Â Â Â I combined the like terms above.
    - 1610 = -1610           I am eliminating the constant, 1610, on the left side of the equation.
               Â
5.25a       = 1533
5.25a/5.25 Â Â = 1533/5.25
a = 292
So, now I have found the number of adult tickets, 292. Â Therefore, 292 adult tickets were sold.
Now let's check. Â Now that we know the value of a of 292, we can plug it into our equations, a + c = 460 and 8.75a + 3.50c = 3143:
292 + c = 460
(8.75 * 292) + 3.50c = 3143
Now, we need to find the value of c in the first equation so that we can plug it into the second equation:
292 + c = 460
-292 Â Â = -292
c = Â 168
(8.75 * 292) + (3.50 * 168) = 3143
2555 + 588 = 3143
3143 = 3143 Â check!
ANOTHER WAY:let a = (adult tickets sold) and c = (childrens tickets sold)
so if 460 tickets total were sold, that means that the sum of the adult and childrens tickets were 460. translated into algebra, it is:
460 = a + c
if there was a total of 3143 dollars, and each adult ticket cost 8.75, each childs ticket cost 3.50, that translates into this equation:
8.75 * a + 3.50 * c = 3143
sub out c and solve for a, and remember order of operations (multiply before you add or subtract)
ANOTHER WAY: Let's use A to represent the number of adult tickets sold, and C for the number of children's tickets sold. We know the cost of each ticket, and the total amount of sales. We also know how many tickets were sold. Let's write the known information in equation form. A + C = 460 <-- Total number of tickets sold, adult and children combined 8.75A + 3.50C = 3143 <-- Multiply adult tickets times the cost of an adult ticket, and repeat for children's tickets. The sum of both is the total sales amount. Solving for A in the first equation is easy, just subtract C from both sides: A + C - C = 460 - C A = 460 - C Substitute this into the second equation, and we'll now have one equation and one variable: 8.75(460-C) + 3.50C = 3143 Multiply out: 8.75*460 - 8.75C + 3.50C = 3143 <-- 8.75*460=4025 4025 - 8.75C + 3.50C = 3143 Next add our 2 C terms together: 4025 - 5.25C = 3143 Add 5.25C to both sides: 4025 - 5.25C + 5.25C = 3143 + 5.25C 4025 = 3143 + 5.25C Subtract 3143 from both sides: 4025 - 3143 = 3143 - 5.25C - 3143 882 = 5.25C Divide through by 5.25: 882/5.25 = 5.25C/5.25 168 = C Recall that A = 460 - C, so A = 460 - 168 = 292. So 292 adult tickets and 168 child tickets were sold
Hope you understand! Plz mark BRAINLIEST!
