Let x be number of widgets produced in 3 1/2 weeks.
The proportion therefore between the two ratios is
[tex]\frac{x\text{ widgets}}{3\frac{1}{2}\text{ weeks}}=\frac{1250\text{ widgets}}{1\text{ week}}[/tex]
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.
[tex]\begin{gathered} 3\frac{1}{2}\text{ weeks}\Big(\frac{x\text{ widgets}}{3\frac{1}{2}\text{ weeks}}=\frac{1250\text{ widgets}}{1\text{ week}}\Big)3\frac{1}{2}\text{ weeks} \\ \cancel{3\frac{1}{2}\text{ weeks}}\Big{(}\frac{x\text{ widgets}}{\cancel{3\frac{1}{2}\text{ weeks}}}=\frac{1250\text{ widgets}}{1\cancel{\text{week}}}\Big{)}3\frac{1}{2}\cancel{\text{week}} \\ x\text{ widgets }=1250\cdot3\frac{1}{2}\text{ widgets} \\ x\text{ widgets }=1250\cdot3.5\text{ widgets} \\ x\text{ widgets }=4375\text{ widgets} \end{gathered}[/tex]
Therefore, they can produce 4375 widgets in 3 1/2 weeks.
