Youssef is taking a trip on an airplane. He knows that to avoid extra fees his suitcase must weigh under 50 pounds. The suitcase with his clothes weighs 35 pounds. He has room, so he decides to pack some books for his trip, too. Each book weighs on average 1.2 pounds. How many books could he bring on the trip? He writes the inequality 1.2b+35<50 , where b equals the number of books, to help figure this out. Solve his inequality. Use the letter b as your variable and write your b term first.
Note: You will find the option to add a >
, <
, ≥
, or ≤
symbol in the Comparison (<)
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(1 point)
1.2b + 35 < 50
Subtract 35 from both sides:
1.2b < 50 - 35
1.2b < 15
Divide both sides by 1.2:
b < 15 / 1.2
b < 12.5
So, Youssef could bring a maximum of 12 books on the trip.
Inequalities Unit Test
12 of 1512 of 15 Items
Question
Marjam has a goal of taking at least 10,000 steps today. According to her pedometer, she got 2,500 steps in the morning. There are 10 hours left in the day. How many steps will she need to get each hour (assume she walks the same number of steps each hour) for the rest of the day to meet her goal? Solve this problem. Which graph most clearly communicates the solution?(1 point)
Responses
A number line ranges from 0 to 900 in 100 unit increments. An open point is labeled and plotted at 750. A line extends from that point to the right and goes past 900.
Image with alt text: A number line ranges from 0 to 900 in 100 unit increments. An open point is labeled and plotted at 750. A line extends from that point to the right and goes past 900.
A number line is marked with 10 equidistant tick marks. An open point is plotted halfway between the eighth and ninth tick marks from the left. A line extends from that point to the right and goes past the last tick mark.
Image with alt text: A number line is marked with 10 equidistant tick marks. An open point is plotted halfway between the eighth and ninth tick marks from the left. A line extends from that point to the right and goes past the last tick mark.
A number line ranges from 0 to 900 in 100 unit increments. An open point is labeled and plotted at 750. A line extends from that point to the right and goes past 900.
Image with alt text: A number line ranges from 0 to 900 in 100 unit increments. An open point is labeled and plotted at 750. A line extends from that point to the right and goes past 900.
An illustration shows a number line labeled Marjam’s Steps per Hour for the Remainder of the Day. The number line ranges from 0 to 900 in 100 unit increments. A closed point is plotted at 750. A line extends from that point to the right and goes past 900.
Image with alt text: An illustration shows a number line labeled Marjam’s Steps per Hour for the Remainder of the Day. The number line ranges from 0 to 900 in 100 unit increments. A closed point is plotted at 750. A line extends from that point to the right and goes past 900.
To find out how many steps Marjam will need to get each hour for the rest of the day, we need to subtract the steps she already took (2,500) from her goal (10,000) and then divide the remaining steps by the number of hours left (10).
Remaining steps = Goal - Steps in the morning = 10,000 - 2,500 = 7,500
Steps per hour = Remaining steps / Hours left = 7,500 / 10 = 750
Therefore, Marjam will need to get 750 steps each hour for the rest of the day to meet her goal.
The graph that most clearly communicates this solution is:
An illustration shows a number line labeled Marjam’s Steps per Hour for the Remainder of the Day. The number line ranges from 0 to 900 in 100 unit increments. A closed point is plotted at 750. A line extends from that point to the right and goes past 900.
To solve the inequality 1.2b + 35 < 50, we need to isolate the variable b.
Step 1: Start by subtracting 35 from both sides of the inequality:
1.2b + 35 - 35 < 50 - 35
Simplifying, we have:
1.2b < 15
Step 2: Divide both sides of the inequality by 1.2 to solve for b:
(1.2b)/1.2 < 15/1.2
Simplifying, we get:
b < 12.5
Since b represents the number of books Youssef can bring, he can bring a maximum of 12 books on the trip to ensure his suitcase weighs under 50 pounds.