I have been stuck on this lesson for over a week on accelus. I've tried to get my dads help, i watched the help video over 5 times, and looked on youtube for answers, but NOTHING has worked. It's solving real world systems of equations via elimination.
Here is the question:
A sporting event hels at a high school had 135 attendees. The event earned a total of $930. Admission to the event was $10 dollars for adults and $4 for students. How many adults (a) and how many students (s) attended?
a + s = 135
10a + 4s = $930
That the only question i have, i really need to know how to solve this. I also need help with the ones with decimals. Basically its ones like that except they have decimals at the end so you have to multiply a side. Those are the hardest. Please help me!
I made a few grammatical errors, sorry.
ok with
a + s = 135
10a + 4s = 930
multiply the first by 4, repeat the 2nd
4a + 4s = 540
10a + 4s = 930
now subtract them:
6a = 390
a = 65
sub into the first:
65 + s = 135
s = 70
all done, just state the conclusion.
Thank you, @mathhelper, but what about decimals? For example:
Jared bought 7 cans of paint. A can of red pain costs $3.75. A can of black paint costs $2.75. Jared spent 22.25 in all. How many cans of black (b) and how many cans of red (r) did he buy?
R + b = 7
3.75r + 2.75b = 22.25
I already know the answer to this ( i guessed it) but i don't really know how to solve it.
you can use elimination, as shown on the first problem. Decimals are no problem. Use them just like any other numbers. But your equations make substitution also very easy.
since r+b = 7, b = 7-r
So, using that in the 2nd equation,
3.75r + 2.75(7-r) = 22.25
3.75r + 19.25 - 2.75r = 22.25
1.00r = 3.00
or, r=3
I can definitely help you with solving this system of equations via elimination.
To solve the system of equations you provided:
1. Start by eliminating one of the variables from the equations. In this case, it is convenient to eliminate variable 'a'.
Multiply the first equation by 10 to make the coefficients of 'a' in both equations the same:
10(a + s) = 10(135)
10a + 10s = 1350
Now you have two equations:
10a + 10s = 1350 (equation 1)
10a + 4s = 930 (equation 2)
2. Subtract equation 2 from equation 1 to eliminate 'a':
(10a + 10s) - (10a + 4s) = 1350 - 930
Simplify the equation:
10s - 4s = 420
Combine like terms:
6s = 420
3. Solve for 's' by dividing both sides of the equation by 6:
6s = 420
s = 420 / 6
s = 70
So, there were 70 students in attendance.
4. Substitute the value of 's' back into one of the original equations to solve for 'a':
a + 70 = 135
Subtract 70 from both sides:
a = 135 - 70
a = 65
There were 65 adults in attendance.
Therefore, the solution to the system of equations is:
a = 65 (adults in attendance)
s = 70 (students in attendance)
To solve similar problems with decimals, you follow the same steps, but you may need to be careful with decimal placement and perform any necessary multiplication or division.