Question

1. your brother has $2,000 saved for a vacation. his airplane ticket is $637. write and solve an inequality to find out how much he can spend for everything else.

1. your local bank offers free checking for accounts with a balance of at least $500. suppose you have a balance of $516.46 and you write a check for $31.96. how much do you need to deposit to avoid being charged a service fee?

Explanation:

Problem 5

Step1: Define variable

Let \( x \) be the amount he can spend for everything else. The total amount he can spend (ticket + everything else) should be less than or equal to his savings. So the inequality is \( 637 + x \leq 2000 \).

Step2: Solve the inequality

Subtract 637 from both sides: \( x \leq 2000 - 637 \)
Calculate \( 2000 - 637 = 1363 \). So \( x \leq 1363 \).

Step1: Calculate new balance after check

Current balance is \$516.46, after writing a check for \$31.96, the new balance is \( 516.46 - 31.96 = 484.5 \).

Step2: Let \( d \) be the deposit amount. We need the new balance (after deposit) to be at least \$500. So the inequality is \( 484.5 + d \geq 500 \).

Step3: Solve for \( d \)

Subtract 484.5 from both sides: \( d \geq 500 - 484.5 \)
Calculate \( 500 - 484.5 = 15.5 \). So \( d \geq 15.5 \).

Answer:

The inequality is \( 637 + x \leq 2000 \) and the solution is \( x \leq 1363 \), meaning he can spend at most \$1363 for everything else.

Problem 6