Question
Sam is buying packages with 9 beads each. His mom bought him 63 more beads. Now, he has 153 beads. How many packages did he buy? Use algebra to determine the answer.(1 point)
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Let x be the number of packages Sam bought.
Sam initially had 9x beads before his mom bought him more.
After his mom bought him 63 more beads, he had 9x + 63 beads.
According to the problem, he now has 153 beads, so we can write the equation:
9x + 63 = 153
Subtracting 63 from both sides of the equation, we get:
9x = 90
Dividing both sides of the equation by 9, we get:
x = 10
Therefore, Sam bought 10 packages. Answer: \boxed{10}.
Triana is on a 120-mile four-day bike ride. On the first day she travels 24 miles. She would like to travel equal amounts over the remaining three days. How far will she travel on each of those three days? Write and solve an equation of the form px+q=r . Then write a sentence to explain your answer.(4 points)
Let x represent the distance Triana will travel on each of the remaining three days.
Since she traveled 24 miles on the first day, the total distance she will travel on the four-day ride is 24 + 3x.
According to the problem, the total distance is 120 miles, so we can write the equation:
24 + 3x = 120
Subtracting 24 from both sides of the equation, we get:
3x = 96
Dividing both sides of the equation by 3, we get:
x = 32
Therefore, Triana will travel 32 miles on each of the remaining three days. Answer: \boxed{32}.