Unique Uniforms Company charges $17.75 per cap plus a design fee of $30. logos Direct Inc charges $15.50 per cap plus a delivery fee of $48. For what number of caps ordered would the cost be the same from both vendors?

Question

anonymous · Answer

Let n be the number of caps.  Solve the following for n:$$30+\frac{1775}{100}n=\frac{1550}{100}n+48 $$$$n=8 $$

anonymous · Answer

Did you just randoly divide by 100 to get the answer?

anonymous · Answer

Multiply each side by 100 to get rid of the fractions.   By using fractions in the equation setup, the solution will always be symbolically exact.

anonymous · Answer

Okay so you added 30 plus 17.75 then divided that by 100 then you added 15.50 plus 48 and subtracted the two answers?

anonymous · Answer

$$100\left(30+\frac{1775}{100}n\right)=\left(\frac{1550}{100}n+48\right)100 $$$$3000+1775 n=4800+1550 n$$$$1775 n-1550 n=4800-3000 $$$$225 n=1800$$$$n=\frac{1800}{225}=8 $$

anonymous · Answer

Ooooh okay I get it now thanks soo much :) you really helped me out

anonymous · Answer

You are welcome.

anonymous · Answer

And thank you for the medal.

anonymous · Answer

No problem you deserved it :)