Answer:
#3:
8x+56=80
2x=6
x=3
#4
Fabian can make 3 batches of soup
Step-by-step explanation:
Equations
We'll use some algebra rules to set, simplify, and solve equations. LEt's start with question #3
We have the equation
[tex]\displaystyle \frac{1}{4}(8x+56)=20[/tex]
From that expression, we'll try to find out which other(s) are equivalent. If we operate the fraction by the parentheses, we have
[tex]2x+14=20[/tex]
This expression eliminates the second alternative. If we had multiplied all the equation by 4 instead of performing the product:
[tex]\displaystyle 4*\frac{1}{4}(8x+56)=20*4[/tex]
[tex]8x+56=80[/tex]
This is equivalent to the first option. It's correct and should be checked out. Taking from this equation
[tex]2x+14=20[/tex]
If we subtract 2x, we have
[tex]14=20-2x[/tex]
This is different from the first option in the second row. It should not be checked out
Solving for x
[tex]2x=6[/tex]
This is equivalent to the last option. Finally,
[tex]x=3[/tex]
which is equal to the 3rd option, first row. To summarize, all the equations equivalent to the first given are
8x+56=80
2x=6
x=3
Question #4
From the 10 pounds of tomatoes Fabian harvested, he sets aside 2.8 pounds to make spaguetti sauce. This leaves him with (10 - 2.8) pounds of tomatoes to make x batches of soup, each one of which needs 2 2/5 pounds of tomatoes. The equation to solve is
[tex]\displaystyle \frac{10-2.8}{x}=2 \frac{2}{5} =\frac{12}{5}[/tex]
Solving for x
[tex]\displaystyle \frac{10-2.8}{\frac{12}{5}}=x=\frac{5\times 7.2}{12}=3[/tex]
Fabian can make 3 batches of soup
