Keith has 40-pound bags of mulch in his truck that weigh a total of 3600 pounds. His Owner’s Manual lists the truck’s capacity a
1 answer:
Answer:
Keith must remove 90-75 = 15 bags in order to meet the weight requirements
Step-by-step explanation:
This problem can be solved by consecutive rules of three problem.
Rule of three problem:
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.
In this problem, the measures are:
- The number of bags
- The total weight
As the number of bags increases, so do the total weight. So, the relationship between the measures is direct.
To know how many bags does Keith need to remove in order to meet the weight requirements, we first need to know how many bags are in the truck currently.
The problem states that each bag weighs 40 pounds and the weight of the truck is 3600 pounds, so:
1 bag - 40 pounds
x bags - 3600 pounds
40x = 3600
x = 90.
Keith currently has 90 bags in the truck.
Now, we have to know how much bags he can have in the truck, that is, 3000 pounds worth of bags. So:
1 bag - 40 pounds
x bags - 3000 pounds
40x = 3000
x = 75.
The truck's capacity is at most 75 bags.
So, Keith must remove 90-75 = 15 bags in order to meet the weight requirements
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Answer:
a. ;
b.
Step-by-step explanation:
We need here to apply the <em>Multiplication Principle </em>or the <em>Fundamental Principle of Counting</em> for each answer. Answer <em>b</em> needs an extra reasoning for being completed.
The <em>Multiplication Principle</em> states that if there are <em>n</em> ways of doing something and <em>m</em> ways of doing another thing, then there are <em>n</em> x <em>m</em> ways of doing both (<em>Rule of product</em> (2020), in Wikipedia).
<h3>In how many ways can ten students line up? </h3>There are <em>ten</em> students. When one is selected, there is no other way to select it again. So, <em>no repetition</em> is allowed.
Then, in the beginning, there are 10 possibilities for 10 students; when one is selected, there are nine possibilities left. When another is selected, eight possibilities are left to form the file, and so on.
Thus, we need to multiply the possibilities after each selection: that is <em>why</em> the <em>Multiplication Principle</em> is important here.
This could be expressed mathematically using n!:
For instance,
So, for the case in question, the <em>ten</em> students can line up in:
ways to line up in a single file.
For this question, we need to consider the former reasoning with extra consideration in mind.
The members of Group 1 can occupy <em>only</em> the following places in forming the file:
<em>places</em>.
The members of Group 2 <em>only</em>:
<em>places</em>.
And the members of Group 3, the following <em>only</em> ones:
<em>places.</em>
Well, having into account these possible places for each member of G1, G2 and G3, there are: <em>10! ways</em> for lining up members of G1; <em>10! ways</em> for lining up members of G2 and, also, <em>10! ways</em> for lining up members of G3.
After using the <em>Multiplication Principle</em>, we have, thus:
<em>ways the students can line up to come in from recess</em>.