It takes a florist 3h 15min to make 3 small centerpieces and 3 large cebterpieces. It takes 6h 20min to make 4 small centerpieces abd 7 large centerpieces. How long does it take to make each small centerpiece and each large centerpiece? Write and solve a system of equations to find your answer.

Question

It takes a florist 3h 15min to make 3 small centerpieces and 3 large cebterpieces. It takes 6h 20min to make 4 small centerpieces abd 7 large centerpieces. How long does it take to make each small centerpiece and each large centerpiece? Write and solve a system of equations to find your answer.

Answer 1

remember rate*time=pieces

3.25=S*3+L*2 where S, L are the time for small, and large.
6.33333=4S+7L

solve for S, and L

Answer 2

Thank you.

Answer 3

To solve this problem, we can assign variables to the time it takes to make each small centerpiece and each large centerpiece.

Let's say it takes x hours and y minutes to make one small centerpiece, and it takes a hours and b minutes to make one large centerpiece.

From the first sentence, we know that it takes the florist 3 hours and 15 minutes to make 3 small centerpieces and 3 large centerpieces. Converting 3 hours and 15 minutes to minutes, we get: 3 hours * 60 minutes/hour + 15 minutes = 195 minutes.

So, using the variables we defined, we can write the first equation as:

3(x + a) + 3(y + b) = 195 Equation 1

From the second sentence, we know that it takes the florist 6 hours and 20 minutes to make 4 small centerpieces and 7 large centerpieces. Converting 6 hours and 20 minutes to minutes, we get: 6 hours * 60 minutes/hour + 20 minutes = 380 minutes.

So, using the variables we defined, we can write the second equation as:

4(x + a) + 7(y + b) = 380 Equation 2

We now have a system of two equations with two variables. We can solve this system to find the values of x, y, a, and b.

To solve this system, we can use the method of substitution or elimination. Let's use the method of substitution:

From Equation 1, we can solve for x + a:

x + a = (195 - 3(y + b))/3

Substituting this expression into Equation 2, we get:

4[(195 - 3(y + b))/3] + 7(y + b) = 380

Now we can solve for y + b:

4(195 - 3(y + b)) + 21(y + b) = 1140

Simplifying this equation gives us:

780 - 12(y + b) + 21(y + b) = 1140

780 + 9(y + b) = 1140

9(y + b) = 360

Dividing both sides by 9, we find:

y + b = 40

Now we have the value of y + b.

We can substitute this value back into Equation 1 or Equation 2 to find the value of x + a. Then, we can use the values of x + a and y + b to find the individual values of x, y, a, and b.

From there, you can find the time it takes to make each small centerpiece and each large centerpiece.