Question

sketch a model to estimate. then determine each solution and write an equation.

1. the temperature in wichita, kansas, is $-3^circ$c. the temperature in alejandros hometown is $18^circ$ colder than that. what is the temperature in alejandros hometown?

1. to qualify to compete in the high jump finals, athletes must jump a certain height in the semi-finals. paola jumped $2\frac{3}{8}$ inches below the qualifying height, but her friend elena made it to $1\frac{5}{6}$ inches over the qualifying height. how much higher was elenas semi-final jump compared with paolas?

1. the down under roller coaster rises up to 65.8 feet above the ground before dropping 90 feet into an underground cavern. describe the height of the roller coaster at the bottom of the cavern.

Explanation:

Problem 3

Step1: Identify the operation

The temperature in Alejandro’s hometown is 18° colder than -3°C, so we need to subtract 18 from -3, or use addition of a negative: \(-3 + (-18)\).

Step2: Perform the calculation

Using the rule for adding negative numbers: \(-3 + (-18) = -(3 + 18) = -21\). The equation is \(T = -3 - 18\), where \(T\) is the temperature in Alejandro’s hometown.

Step1: Define the qualifying height as \(h\)

Paola’s jump height: \(h - 2\frac{3}{8}\). Elena’s jump height: \(h + 1\frac{5}{6}\).

Step2: Find the difference

Subtract Paola’s height from Elena’s: \((h + 1\frac{5}{6}) - (h - 2\frac{3}{8})\). The \(h\) terms cancel: \(1\frac{5}{6} + 2\frac{3}{8}\).

Step3: Convert to improper fractions

\(1\frac{5}{6} = \frac{11}{6}\), \(2\frac{3}{8} = \frac{19}{8}\). Find a common denominator (24): \(\frac{11}{6} = \frac{44}{24}\), \(\frac{19}{8} = \frac{57}{24}\).

Step4: Add the fractions

\(\frac{44}{24} + \frac{57}{24} = \frac{101}{24} = 4\frac{5}{24}\).

Step1: Identify the operations

The roller coaster rises 65.8 feet (positive) then drops 90 feet (negative). The height at the bottom is \(65.8 - 90\).

Step2: Perform the subtraction

\(65.8 - 90 = -(90 - 65.8) = -24.2\).

Answer:

The temperature is \(-21^\circ\)C, and the equation is \(T = -3 - 18\) (or \(T = -3 + (-18)\)).

Problem 4