Chapter 6, Problem 25CR

To determine

To write: and solve a system of equation for the given situation.

Answer to Problem 25CR

The florist takes 25 min to complete one small centerpiece and 40 min to complete one large centerpiece.

Explanation of Solution

Given:

Time taken by the florist to make 3 large centerpieces and 3 small centerpieces $=$ 3 h 15 min $=$ 195 min

Time taken by the florist to make 7 large centerpieces and 4 small centerpieces $=$ 6 h 20 min $=$ 380 min

Calculation:

Let $x$ be the time taken by the florist to make 1 small centerpiece.

Let $y$ be the time taken by the florist to make 1 large centerpiece.

Now, according to the question,

The florist takes 195 min to make 3 large centerpieces and 3 small centerpieces.

So, the equation for the above situation will be,

  $\Rightarrow 3x+3y=195$

  $\Rightarrow 3(x+y)=195$

  $\Rightarrow x+y=\frac{195}{3}$

  $\Rightarrow x+y=65$

  $\Rightarrow x=65-y$ ….(i)

Now, according to the question,

The florist takes 380 min to make 7 large centerpieces and 4 small centerpieces.

So, the equation for the above situation will be,

  $\Rightarrow 4x+7y=380$ ….(ii)

For solving the system of equations,

Put equation (i) in equation (ii),

  $\Rightarrow 4(65-y)+7y=380$

  $\Rightarrow 260-4y+7y=380$

  $\Rightarrow 3y=120$

  $\Rightarrow y=40$

Now, putting $y=40$ in equation (i),

  $\Rightarrow x=65-40$

  $\Rightarrow x=25$

  $\therefore x=$ 25 min and $y=40$ min

Conclusion:

Hence, the florist takes 25 min to complete one small centerpiece and 40 min to complete one large centerpiece.