Abby walked 1 1/6 miles on Monday, 2 1/3 miles on Tuesday, and 4 1/12 miles on Wednesday. What is the total distance Abby walked
1 answer:
You might be interested in
Answer:
Ginny made a mistake in step 1 when she identified b = 31. It should be b=-31
Step-by-step explanation:
Ginny factored as shown:
ac = –180 and
b = 31
36(–5) = –180 and 36 + (–5) = 31
+ 36x – 5x – 30
6x(x + 6) – 5(x + 6)
(x + 6)(6x – 5)
b is the coefficient of x and from the trinomial , b=-31.
Therefore Ginny made a mistake in step 1 when she identified b = 31. It should be b = –31.
The correct steps are: :
ac = –180 and
b = -31
36(–5) = –180 and -36+5 = -31
Answer:
Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.
Step-by-step explanation:
Let 10-oz, 14-oz, and 20-oz coffees be represented by the variables <em>a, b</em>, and <em>c</em>, respectively.
Since a total of 14 cups of coffee was served:
A total of 204 ounces of coffee was served. Therefore:
A total of $16.70 was collected. Hence:
This yields a triple system of equations. In order to solve a triple system, we should isolate the system to only two variables first.
From the first equation, let's subtract <em>a</em> and <em>b</em> from both sides:
Substitute this into both the second and third equations:
And:
In this way, we've successfully created a system of two equations, which can be more easily solved. Distribute:
For the Second Equation:
And for the Third:
We can solve this using substitution. From the second equation, isolate <em>a: </em>
<em /><em />
Substitute into the third:
Distribute and simplify:
Therefore:
Using the equation for <em>a: </em>
<em /><em />
<em />
And using the equation for <em>c: </em>
<em /><em />
<em />
Therefore, Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.