Question

Q. As a project manager, you need to plan production runs over the next 3 1/2weeks. If your team is able to produce 1250 widgets in one week, how manywidgets can they produce in 3 1/2 weeks?

Answer 1

Let x be number of widgets produced in 3 1/2 weeks.

The proportion therefore between the two ratios is

`\frac{x\text{ widgets}}{3(1)/(2)\text{ weeks}}=\frac{1250\text{ widgets}}{1\text{ week}}`

To solve for the number of widgets they can produce, multiply both sides by 3 1/2, to cancel out the denominator on the left side of the proportion.

`\begin{gathered} 3(1)/(2)\text{ weeks}\Big(\frac{x\text{ widgets}}{3(1)/(2)\text{ weeks}}=\frac{1250\text{ widgets}}{1\text{ week}}\Big)3(1)/(2)\text{ weeks} \\ \cancel{3(1)/(2)\text{ weeks}}\Big{(}\frac{x\text{ widgets}}{\cancel{3(1)/(2)\text{ weeks}}}=\frac{1250\text{ widgets}}{1\cancel{\text{week}}}\Big{)}3(1)/(2)\cancel{\text{week}} \\ x\text{ widgets }=1250\cdot3(1)/(2)\text{ widgets} \\ x\text{ widgets }=1250\cdot3.5\text{ widgets} \\ x\text{ widgets }=4375\text{ widgets} \end{gathered}`

Therefore, they can produce 4375 widgets in 3 1/2 weeks.