Laura is the fund-raising manager for a local charity. She is ordering caps for an upcoming charity walk. The company that makes the caps charges $6 per cap plus a $25 shipping fee. Laura has a budget of $1,000. What is the greatest number of caps she can buy?
Answer:
162 caps.
Step-by-step explanation:
Let x be the number of caps.
We have been given that cost of one cap is $6, so cost of x caps will be equal to 6x.
We are also told that the company charges an amount of $25 for shipping, so total cost of buying x caps will be equal to the cost of x caps plus shipping charges (\(6x+25\)).
Since Laura has a budget of $1,000, so cost of x caps will be less than or equal to 1,000. We can represent this information in an equation as:
\(6x+25\leq 1,000\)
Now let us solve for x.
\(6x+25-25\leq 1,000-25\)
\(6x\leq 975\)
Let us divide both sides of our inequality by 6.
\(\frac{6x}{6}\leq \frac{975}{6}\)
\(x\leq 162.5\)
Since we can not buy 0.5 of a cap, so the greatest number of caps Laura can buy is 162 caps.