12.3 Activity: 5 dollars
1 answer:
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Answer:
28 portraits
Step-by-step explanation:
Let's first figure out how many portraits Lamy can paint in 1 week, which is his <u>unit rate</u>. To calculate this, we just have to divide the number of portraits he paints by the amount of time it takes him to paint them.
In this case, the former quantity is 84 portraits, and the latter quantity is 6 weeks, so his unit rate is = 14 paintings per week.
Now, we know that in 1 week, Lamy can paint 14 portraits. Therefore, since this is a <u>directly proportional relationship</u>, all we have to do to find how many portraits he can paint is 2 weeks is double the unit rate. This is because in a directly proportional relationship, if you multiply one variable by a number, you have to multiply the other by the same number to maintain equality, and here we are multiplying weeks by 2 so we need to multiply paintings by 2 as well.
Thus, Lamy can paint 14 · 2 = 28 paintings in 2 weeks.
Hope this helps!
Answer:
We can only be certain that <em>a</em> weighs 12.
There are infinitely many possiblities for <em>b</em> and <em>c</em>.
Step-by-step explanation:
We have the equation:
Each variable indicates a weight.
We would like to determine the weights of each variable (if possible).
First, we can rearrange the equation to acquire:
We can combine like terms:
Notice that both sides have 2<em>b</em> and 3<em>c</em>. Therefore, it is possible for us to cancel them since each nullify the other side. So, we will subtract 2<em>b</em> and 3<em>c</em> from both sides. This yields:
Therefore, we can solve for <em>a</em>. Subtract 2<em>a</em> from both sides:
Hence, the weight of <em>a</em> is 12.
Using the newly acquired information, we can go back to our simplified equation:
Since <em>a</em> is 12:
Evaluate:
Simplify:
We can subtract 36 from both sides:
As you can see, this is a true statement.
Since this is a true statement, there are infinitely many possible values for <em>b</em> and <em>c</em>.
Therefore, the only weight we are <em>certain</em> of knowing is weight <em>a</em> weighing 12.