Question

practice
solve each problem by first writing an inequality.

1. gabe went to the amusement park with $40 to spend. his ticket cost $26.50. determine how much gabe can spend on souvenirs and snacks. then interpret the solution. (example 1)
2. drew practices piano at least 45 minutes per day. he has already practiced 18.5 minutes today. determine how much longer he will have to practice. then interpret the solution. (example 1)
3. a dolphin is swimming at a depth of -50 feet and then ascends a certain number of feet to a depth above -35 feet. determine the number of feet the dolphin ascended. then interpret the solution. (example 1)
4. elena’s account balance with her parents is -$5.50. she adds a certain amount of money to her balance by mowing the lawn. elena now has an account balance less than $20. determine a possible amount she earned mowing the lawn. then interpret the solution. (example 1)
5. linda has two cats. the difference in weight of her maine coon and siberian is at least 6 pounds. linda’s siberian has a weight of $8\frac{3}{4}$ pounds. determine the possible weight of the maine coon. then interpret the solution. (example 2)
6. the hendersons have a sedan and a minivan. the difference in mileage of the two vehicles is greater than 4500 miles. the minivan has 12,755.25 miles. determine the possible number of miles on the sedan. then interpret the solution. (example 2)
7. the difference between the monthly high and low temperatures was less than 27° fahrenheit. the monthly low temperature was -2° fahrenheit. determine the possible monthly high temperature. then interpret the solution. (example 2)

test practice

1. open response teddy has two piggy banks. the difference in the amount of money between the two banks is no more than $10. one piggy bank has $7.31 in it. determine the possible amount of money in the other piggy bank. then interpret the solution.

Explanation:

Let's solve problem 1 step by step:

Step 1: Define the variable and write the inequality

Let \( s \) be the amount Gabe can spend on souvenirs and snacks. The total amount he can spend (ticket + souvenirs/snacks) must be less than or equal to $40. So the inequality is:
\( 26.50 + s \leq 40 \)

Step 2: Solve the inequality

Subtract 26.50 from both sides:
\( s \leq 40 - 26.50 \)
\( s \leq 13.50 \)

Interpretation of the solution:

Gabe can spend at most $13.50 on souvenirs and snacks. This means that if he spends $13.50 or less on these items, the total amount he spends (ticket + souvenirs/snacks) will not exceed the $40 he has.

Answer:

Gabe can spend at most \(\$13.50\) on souvenirs and snacks. The inequality is \(26.50 + s \leq 40\) with solution \(s \leq 13.50\), meaning his spending on souvenirs/snacks must be \(\$13.50\) or less to stay within his \(\$40\) budget.