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Can Anyone On Here Help Me Solve This Question Please?
13 Answers
The local soccer team club spent $675 on tickets to a professional soccer game. If the club bought three fewer $15 tickets than four-fifths the number of $12 tickets, how many tickets of each type did the club buy?
Answers
30 tickets @ $12 and 21 tickets @ $15
19:10 Sun 13th Sep 2015
and if you need the working out:
Let x = number of $15 tickets and y = number of $12 tickets.
We have:
15x + 12y = 675
and:
x + 3 = (4/5)y ------> rearranging this gives 15x + 45 = 12y
Combine this with above equation gives:
12y - 45 + 12y = 675
24y = 675 + 45
24y = 720
y = 30
and
x + 3 = (4/5)30
x = 24 - 3
x = 21
Let x = number of $15 tickets and y = number of $12 tickets.
We have:
15x + 12y = 675
and:
x + 3 = (4/5)y ------> rearranging this gives 15x + 45 = 12y
Combine this with above equation gives:
12y - 45 + 12y = 675
24y = 675 + 45
24y = 720
y = 30
and
x + 3 = (4/5)30
x = 24 - 3
x = 21
I needed 15x in the equation, so I could substitute it into the original equation.
We have:
15x + 45 = 12y. Re arranging gives, 15x = 12y - 45
Now in the original equation, we have:
15x + 12y = 675
So instead of writing 15x, we put 12y - 45 in its place, so:
12y - 45 + 12y = 675
Rearranging this gives 24y = 720 -----> y = 30
We have:
15x + 45 = 12y. Re arranging gives, 15x = 12y - 45
Now in the original equation, we have:
15x + 12y = 675
So instead of writing 15x, we put 12y - 45 in its place, so:
12y - 45 + 12y = 675
Rearranging this gives 24y = 720 -----> y = 30
>The 15 i'm multiplying to both sides is just the $15 dollar tickets right?
You can multiply both sides of an equation by any number and the equality still applies. 15 was chosen by Gizmonster for the reason he has now given, but he could have chosen any number that eliminated the fractions (as it's easier to deal with whole numbers) , but Gizmonster's aproach made it easier to solve the simultaneous equations in one step
You can multiply both sides of an equation by any number and the equality still applies. 15 was chosen by Gizmonster for the reason he has now given, but he could have chosen any number that eliminated the fractions (as it's easier to deal with whole numbers) , but Gizmonster's aproach made it easier to solve the simultaneous equations in one step