Final answer:
The inequality for the fishing equipment budget problem is 0.50h + 0.35s ≤ 12, where h is the number of hooks and s is the number of sinkers. Two solutions to this problem include buying 10 hooks and up to 20 sinkers, or 5 sinkers and up to 20 hooks while staying within a $12 budget.
Step-by-step explanation:
The question involves setting up and solving an inequality with a budget constraint for purchasing fishing equipment, specifically hooks and sinkers. Let's denote the number of hooks to be bought as h and the number of sinkers as s. The price per hook is $0.50 and per sinker is $0.35. The inequality representing the situation with a budget of $12 is:
0.50h + 0.35s ≤ 12
To graph this inequality, we would plot the line 0.50h + 0.35s = 12 on the hs-plane (where h is on the x-axis and s is on the y-axis) and shade the area that satisfies the inequality, which is below and including the line. The intercepts can be found by setting h and s to zero in turn to get the intercepts (24,0) and (0,34.29), rounding to two decimal places.
For part b, here are two solutions: Suppose you purchase 10 hooks. The inequality will be 0.50(10) + 0.35s ≤ 12, which simplifies to 5 + 0.35s ≤ 12. Solving for s, we find that you could buy up to 20 sinkers. Another solution might be purchasing 5 sinkers. The inequality would be 0.50h + 0.35(5) ≤ 12, which simplifies to 0.50h + 1.75 ≤ 12. Solving for h, you can buy up to 20.5 hooks, which you would round down to 20 hooks due to the indivisible nature of the hooks.
These solutions show different combinations of hooks and sinkers one can buy without exceeding the $12 budget. The graph and solutions depict the trade-offs and combinations available within the budget constraint.