There are three parts in common with both expressions. They all have a coefficient, an x, and a y.
1) Start by finding a common factor of the two coefficients, 15 and 20. What is the biggest number that divides them both? Notice that 15 = 5*3 and 20 = 5*4, so that means 5 can be factored out of both.
2) Next find the common factor of the x's. You have x^3 in the first expression and x^4 in the second. x^3 would be the largest expression that divides both so you can factor it out.
3) Find the common factor of the y's. You have y^2 and y^4, making y^2 the largest expression that can be factored out.
That means 5(x^3)(y^2) is the common factor between those two expressions.
I finished the test and here's the answer~!
3x+5y=25.75
8x+2y=29.00
So I first got what x is equal too.
8x+2y=29 8x+2y-2y=29-2y 8x=29-2y 8x/8=29/8-2y/8 x=3.625-0.25y
Next substitute x for the equation.
3(3.625-0.25y)+5y=25.75
10.875-0.75y+5y=25.75
10.875-10.875+4.25y=25.75-10.875
4.25y/4.25=14.875/4.25
y = 3.5
Now substitute y for 3.5.
8x+2(3.5)=29
8x+7-7=29-7
8x/8=22/8
x = 2.75
The price of a flower bouquet would be $2.75. Don't worry I got this question correct. :)
The quantity of each type of seats sold are as follows:
- Movie and a dinner seat = 200
According to the question,there are four times as many 3D, x seats as Dinner and a Movie, y seats.
That is, x = 4y
Also, total seats
= (x) + (y) + (z) = 3000...….............eqn(1)
Also, If the theater brings in $53,000 when tickets to all 3000 seats are sold.
- 20x + 35y + 15z = 53000...........eqn(2)
By substituting 4y for x in equations 1 and 2; we have;
<em>5y + z = 3000</em>..…........eqn(3) and
<em>115y + 15z = 53000</em>.........eqn(4)
By solving equations 3 and 4 simultaneously; we have;
y = 200 and z = 2000
and since x = 4y
x = 800
The quantity of each type of seats sold is as follows:
- Movie and a dinner seat = 200
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