UESTION 49 Ken and Paul each ordered a sandwich at a restaurant. The price of Ken's sandwich was x dollars, and the price of Paul's sandwich was 1 more than the price of Ken's sandwich. If Ken and Paul split the cost of the sandwiches evenly and each paid a 20% tip, which of the following expressions represents the amount, in dollars, each of them paid? (Assume there is no sales tax.) A) 0.2x+0.2 B 0.5x+0.1 C 1.2x+0.6 D) 2.4x+1.2 The mesosphere is the layer of Earth's atmosphere between 50 kilometers and 85 kilometers above Earth's surface.At a distance of 50 kilometers from Earth's surface.the temperature in the mesosphere is -5^circ Celsius, and at a distance of 80 kilometers from Earth's surface the temperature in the mesosphere is -80^circ Celsius.For every additional 10 kilometers from Earth's surface, the temperature in the mesosphere decreases by ko Celsius, where k is a constant. What is the value of k? is document has been created for educational purposes only and meant to be used exclusive CORE - Test Prep and College Counseling.This document may not be distributed or reproo ithout the express written consent of its authors. I: HEART OF ALG EBRA LI NEAR EQUAT IONS The monthly membership fee for an online television and movie service is 9.80 . The cost of viewing television shows online is included in the membership fee but there is an additional fee of 1.50 to rent each movie online. For one month, Jill's membershi and movie rental fees were 12.80 How many movies did Jill rent online that month? A) 1 B 2 C 3 D 4 One of the requirements for becoming a court reporter is the ability to type 225 words per minute Donald can currently type 180 words per minute, and believes that with practice he can increase his typing speed by 5 words per minute each month. Which of the following represents the number of words per minute that Donald believes he will be able to type m months from now? A) 5+180m B) 225+5m C) 180+5m D) 180-5m

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UESTION 49 Ken and Paul each ordered a sandwich at a restaurant. The price of Ken's sandwich was x dollars, and the price of Paul's sandwich was 1 more than the price of Ken's sandwich. If Ken and Paul split the cost of the sandwiches evenly and each paid a 20% tip, which of the following expressions represents the amount, in dollars, each of them paid? (Assume there is no sales tax.) A) 0.2x+0.2 B 0.5x+0.1 C 1.2x+0.6 D) 2.4x+1.2 The mesosphere is the layer of Earth's atmosphere between 50 kilometers and 85 kilometers above Earth's surface.At a distance of 50 kilometers from Earth's surface.the temperature in the mesosphere is -5^circ Celsius, and at a distance of 80 kilometers from Earth's surface the temperature in the mesosphere is -80^circ Celsius.For every additional 10 kilometers from Earth's surface, the temperature in the mesosphere decreases by ko Celsius, where k is a constant. What is the value of k? is document has been created for educational purposes only and meant to be used exclusive CORE - Test Prep and College Counseling.This document may not be distributed or reproo ithout the express written consent of its authors. I: HEART OF ALG EBRA LI NEAR EQUAT IONS The monthly membership fee for an online television and movie service is 9.80 . The cost of viewing television shows online is included in the membership fee but there is an additional fee of 1.50 to rent each movie online. For one month, Jill's membershi and movie rental fees were 12.80 How many movies did Jill rent online that month? A) 1 B 2 C 3 D 4 One of the requirements for becoming a court reporter is the ability to type 225 words per minute Donald can currently type 180 words per minute, and believes that with practice he can increase his typing speed by 5 words per minute each month. Which of the following represents the number of words per minute that Donald believes he will be able to type m months from now? A) 5+180m B) 225+5m C) 180+5m D) 180-5m

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Let's solve each question step by step: ### Question 49 Ken's sandwich price: $ x $ dollars Paul's sandwich price: $ x + 1 $ dollars Total cost of sandwiches: $ x + (x + 1) = 2x + 1 $ They split the cost evenly: $ \frac{2x + 1}{2} = x + 0.5 $ Each paid a 20% tip: $ 0.2(x + 0.5) = 0.2x + 0.1 $ So, the correct answer is: **B) $ 0.5x + 0.1 $** ### Temperature in the Mesosphere At 50 km: $ -5^{\circ} $ Celsius At 80 km: $ -80^{\circ} $ Celsius Temperature decrease per 10 km: $ k $ Temperature change from 50 km to 80 km: $ -80 - (-5) = -75 $ Distance: 30 km (80 - 50) Temperature decrease per 10 km: $ k = \frac{-75}{30} = -2.5 $ So, the value of $ k $ is: **-2.5** ### Online Television and Movie Service Monthly membership fee: $9.80 Additional fee per movie: $1.50 Total cost for one month: $12.80 Let $ m $ be the number of movies rented. Equation: $ 9.80 + 1.50m = 12.80 $ Solve for $ m $: \[ 1.50m = 12.80 - 9.80 \] \[ 1.50m = 3 \] \[ m = \frac{3}{1.50} = 2 \] So, the number of movies Jill rented is: **B) 2** ### Donald's Typing Speed Current speed: 180 words per minute Increase per month: 5 words per minute Typing speed after $ m $ months: $ 180 + 5m $ So, the correct answer is: **C) $ 180 + 5m $**

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