IF you can show the work that would be help full...thanks so much again..
1.timmy has 180 marbles, some plain some colored. if there are 32 more plain the colored marbles, how many colored marbles does he have?
2. a theater sold 900 tickets to a play. floor seats cost $12 each and balcony seats $10 each. total receipts were $9780, how many of each type of tickets were sold
2007-04-04 17:42:15 · 10 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
1.x+(x+32)=180
2x+32=180
2x=148
x=74
2. x+y=900 y=900-x
12x+10y=9780
substitute y into this lower equation to get 12x+(9000-10x)=9780 Therefore, 2x=780 and x=390 y=510
2007-04-04 17:48:20 · answer #1 · answered by bruinfan 7 · 0⤊ 0⤋
1. Let x = number of plain marbles
Let y = number of colored marbles
We know that x + y = 180 marbles
We know that there are 32 more plain than colored
So we know that x= y + 32
Substitute this into the first equation
y + 32 + y = 180
2y = 180 - 32
2y = 148
y = 74 colored marbles
x+ 74 = 180
x = 106 plain marbles
2. We know that there were two types pf tickets sold
Let x = the number of floor seats
Let y = the number of balcony seats
we know that x + y = 900 or that y = 900-x
now form an equation using the cost of the tickets
12x + 10y = 9780 Substitute the value of y into this eqn
12x +10 (900-x) = 9780
12x + 9000 - 10x == 9780
2x = 9780 - 9000
2x = 780
x = 390 f l oor seats
390 + y = 900
y = 510 balcony seats
To check put these values into the eqn with the money to see if it balances.
2007-04-04 18:06:29 · answer #2 · answered by kale_ewart 5 · 0⤊ 0⤋
1. Let x be the number of the colored marbles. Then the number of the plain marbles is x+32.
The sum of the marbles is 180, so you have the equation:
x + (x+32) = 180.
Solve this equation.
2x + 32 = 180
2x = 148
x = 74.
So, he has 74 colored marbles.
2. Let x be the number of floor seats sold. Then the number of balcony seats sold is 900-x.
The total receipts is $9780, so you have the equation:
12x + 10(900-x) = 9780.
Solve this equation.
12x + 9000 - 10x = 9780
2x = 780
x = 390.
So, the number of floor tickets sold is 390 and the number of balcony tickets sold is 900-390, which is 510.
2007-04-04 18:00:00 · answer #3 · answered by hoogiez 1 · 0⤊ 0⤋
1. let x = the number of colored marbles ...
x + (x+32) = 180
where (x+32) is number of plain marbles...
2x + 32 = 180 .. added like terms
2x = 148 ... subtracted 32 from both sides
x = 74 ... divided both sides by 2
2.
let x = number of floor seat tickets
let y = number of balcony seat tickets
x + y = 900
$12*x + $10*y = $9780
so, y = 900 - x ... subtracted x from both sides of first equation
so, substitude in for y in second equation
12*x + 10* (900 - x) = 9780
...
12x + 9000 - 10*x = 9780 .. distribute 10
2x + 9000 = 9780 .... added like terms.. 12x - 10x
2x = 780 ... subtracted 9000 from both sides
x = 390 .. divided both sides by 2 ... this is number of floor...
then
390 + y = 900
y = 510 .. subtract 390 from both sides
2007-04-04 17:52:33 · answer #4 · answered by kerbourchardalan 2 · 0⤊ 0⤋
1)
180-32 = 148
number of coloured marbles = 148/2 = 74
number of plain marbles = 74+32 = 106
2)
assume x tickets were sold for floor seats
hence, (900-x) tickets were sold for balcony seats
therefore,
9780 = 12x + 10(900-x)
9780 = 12x + 9000 - 10x
780 = 2x
x = 390
390 floor seats
510 balcony seats
2007-04-04 17:48:03 · answer #5 · answered by ong_joce 2 · 0⤊ 0⤋
1.
let x = no. of colored marbles
x+32 = no. of plain marbles
x + (x+32) = 180
2x + 32 =180
2x = 180 - 32
2x = 148
x = 74
2.
let x = no. of 12 dollar tickets
900-x = no. of 10 dollar tickes
12x + (900-x)(10) = 9780
12x + 9000 - 10x = 9780
12x - 10x = 9780 -9000
2x = 780
x = 390
900-x = 900-390 = 510
390 -- no. of 12 dollar tickets
510 -- no. of 10 dollar tickets
2007-04-04 18:28:06 · answer #6 · answered by hitherto.24 1 · 0⤊ 0⤋
1. let coloured marbles be x
plain marbles are x+32
x+x+32=180
2x=180-32
2x=148
x=148/2=74
he has 74 coloured marbles
2. let floor tickets sold be x
balcony tickets sold sre 900-x
total cost of floor tickets = x*12=$12x
total cost of balcony tickets = (900-x)*10=$(9000-10x)
12x+9000-10x=9780
2x=9780-9000
2x=780
x=390
floor tickets sold=390
balcony tickets sold=900-390=510
2007-04-04 17:51:33 · answer #7 · answered by Mayank A 3 · 0⤊ 0⤋
1. Let X=Plain, Y=Colored
A: X+Y=180
B: X-Y=32
Solve for X: (Add Y to both sides) X=(Y+32)
Substitute into equation A:
(Y+32) +Y =180
2Y+32=180
2Y=148
Y=74
180 - 74 = 106
X=106
2007-04-04 17:54:35 · answer #8 · answered by Stratman 4 · 0⤊ 0⤋
let the no of coloured marbles be x
so the no of plain marbles will be x+32
so x+x+32=180
2x=148
x=74
no of plain marbles=74
no of coloured marbles=106
let x=no of tickets sold at $12
y=no of tickets sold at $10
so x+y=900
hence 12x+12y=10800 ---------------------------------1
also 12x+10y=9780 ---------------------------------2
subtracting 2 from 1
2y=1020
y=510
so x=390
2007-04-04 17:54:28 · answer #9 · answered by Anonymous · 0⤊ 0⤋
ahh i bear in mind this undemanding algebra from like seventh grade. You upload 2 to each and each and every facet to cancle it on the left facet. then you ought to get x=-x+4. then you upload x to each and each and every facet to get rid of x on the right facet, on the grounds that negative x plus powerful x equals 0. then you could have 2x=4. then you divide each and each and every facet by technique of two to get x by technique of itself. this gives the reply x=2. in case you plug 2 decrease back in for x in the unique equation, you ought to work out -2+2=-2+2. This a real fact on the grounds that 0=0. wish i helped!
2016-12-03 07:45:40 · answer #10 · answered by ? 4 · 0⤊ 0⤋