solve if x=student price and y =adult price and 2y + 5x=77 and 2y + 7x=95 what are the price for admission for both adult and child
if i have 550 students and there are 144 more boys than girls how many girls are in class
Connie, I answered this question for you on Tuesday
http://www.jiskha.com/display.cgi?id=1331674038
REINY, Thank you for your answer and the answer is obviously correct when you go back and do the multiplying ......however , I do not just want the answer, I desperately wish to understand from start to finish how you got the answer. I am sorry if I seem stupid, really , but how did you get 2x = 18 , x=9 where did the 18 come from? I am so confused. Thanks for your help!!!! connie
I thought I showed every step in the solution ....
line them up above each other:
2y + 7x = 95
2y + 5x = 77
now subtract them to get
0 + 2x = 18
(2y-2y=0 , 7x-5x = 2x, 95-77 = 18)
so 2x = 18
divide both sides by 2
2x/2 = 18/2
x = 9
sub that back into one of the original equations
2y + 5(9) = 77
2y + 45 = 77
subtract 45 from both sides
2y + 45 - 45 = 77 - 45
2y = 32
divide by 2
y = 16
so x = 9 and y = 16
To solve for the prices of admission for both adults and children, we need to solve the given system of equations:
2y + 5x = 77 ...(Equation 1)
2y + 7x = 95 ...(Equation 2)
We can use the method of elimination to solve this system.
Step 1: Multiply Equation 1 by 2 to eliminate the y term:
2(2y + 5x) = 2(77)
4y + 10x = 154 ...(Equation 3)
Step 2: Multiply Equation 2 by -2 to eliminate the y term:
-2(2y + 7x) = -2(95)
-4y - 14x = -190 ...(Equation 4)
Step 3: Adding Equation 3 and Equation 4 together to eliminate the y term:
(4y + 10x) + (-4y - 14x) = 154 + (-190)
4y - 4y + 10x - 14x = -36
-4x = -36
Step 4: Divide both sides of the equation by -4 to solve for x:
(-4x) / -4 = (-36) / -4
x = 9
Step 5: Substitute the value of x back into either Equation 1 or Equation 2 to solve for y. Let's use Equation 1:
2y + 5(9) = 77
2y + 45 = 77
2y = 77 - 45
2y = 32
Step 6: Divide both sides of the equation by 2 to solve for y:
(2y) / 2 = 32 / 2
y = 16
Therefore, the price for admission for an adult is $16 and the price for admission for a child is $9.