Afurniture shop refinished chairs. employees use one of two methods to refinish each chair. method one takes 1 hour and the material costs $6. method 2 takes 2.5 hours, and the material costs $4. next week, they plan to spend 157 hours in labor and $568 in material for refinishing chairs. how many chairs should they plan to refinish with each method

To answer this question, we can use a system of equations.  Let's let the number of chairs refinished using method 1 be represented by the variable x, and let the number of chairs refinished using method 2 be represented by the variable y.  We know that method 1 (x) takes 1 hour and method 2 (y) takes 2.5 hours.  If we use these values as coefficients for their respective variables and set their sum equal to the the total number of hours, we get our first equation:

1x + 2.5y = 157

To get our second equation, we use the same method, except this time using 6 as the coefficient for x, 4 as the coefficient for y, and 568 as the sum of these two terms, as modeled below:

6x + 4y = 568

To solve this system of equations, we can use substitution.  To do this, we should solve the first equation for the variable x (get x alone on the left side of the equation):

1x + 2.5y = 157

We should subtract 2.5y from both sides of this equation.

x = 157 - 2.5y

Now, we can substitute this value for x in terms of y into our second equation for the variable x so that we have an equation with only the variable y.

6x + 4y = 568

6(157-2.5y) + 4y = 568

To solve this equation, we must first use the distributive property to get rid of the parentheses on the left side of the equation.

942 - 15y + 4y = 568

Next, we should add the two terms with the variable y together on the left side of the equation.

942 - 11y = 568

After that, we should subtract 942 from both sides of the equation to separate the variables and constants.

-11y = -374

Finally, we should divide both sides of the equation by -11.

y = 34

Now, we can substitute in this value of y into one of our original equations and solve for x.

6x + 4y = 568

6x + 4(34) = 568

Now, we can solve this equation by multiplying together and then subtracting the constants.

6x + 136 = 568

6x = 432

x = 72

Therefore, because x = 72 and y = 34, the furniture shop will refinish 72 chairs using method 1 and 34 chairs using method 2.

Hope this helps!

so far i think you have the right thing going for you just remember soh cah toh

step-by-step explanation:

sine over hypotenuse

cosine   equals adjacent

tangent over hypotenuse