Answer:
Q1 =2.6 pounds of apples, 1.2 pounds of banana.
Q2=1.5 pounds of raisins, 0.6 pounds of granola.
Q3=4.5p+3.75(3.5-p)=9.75.
Q4=20.
Q5=11c+8.75(46-c)=470
Step-by-step explanation:
Let's begin the explanation. These problems are solved by using reduction, equalization or substitution method needed to solve linear system of two equations.
Q1. You have to state the facts: $1.90 per pound of apples, $0.75 per pound of bananas, total weight 3.8 pounds, total cost $5.84.
Next, let's name things, beign pounds of apples = x and pounds of bananas = y.
Now, you have to form the linear system with what you know, and what you've named:
Now you solve. Here I'm going to explain the equalization method.
First thing you need to do is to solve one of the unknowns in both equations. (It has to be the same unknown.)
In this case we will go on solving X from both equations.
Next you have to equalizate the expressions obtained, and solve them:
It's not exactly 2 because I've rounded decimals. But if you do it straight forward it will give you 1.2.
So, now you have the value of bananas pounds (1.2). Next step is to substitute it in any of the equations of the system, and you will get the value of apples pounds.
The solution to question 1 is 2.6 pounds of apples; 1.2 pounds of bananas.
Q2: Similarly to what you have done before, this time x=pounds of raisins, y=pounds of granola.
We will solve this by the substitution method.
Step 1 - Solve 1 equation:
Step 2 - Replace it in the other equation:
Step 3 - Solve the equation:
Step 4 - Replace the value of y in any equation:
The solution to question 2 is 1.5 pounds of raisins; 0.6 pounds of granola.
Q3 Similarly to what you have done before, this time p=pounds of almonds, g=pounds of green beans.
This one is solved by the substitution method explained before.
We set the linear system
Step 1 - Solve 1 equation:
Step 2 - Replace it in the other equation:
You don't need to go on solving this one.
The solution to question 3 is 4.5p+3.75(3.5-p)=9.75
Q4 Once again, state the facts, and set the linear system:
x=Alex work hours, y=Monica work hours
We will solve this by using the reduction method
Step 1 - Make one pair of coefficients of the same variable in negatives of one another.
Step 2 - Add the equations
Step 3 - Solve the new equation
You could continue on, replacing Y value in any equation to get X value, but for this exercise we're done.
The solution to question 4 is 20 hours.
Q5 As we have done before, state the facts, set the linear system:
c=hours worked as an office clerk y=hours worked as a cashier
Remember this kind of exercises are solved by using the substitution method
Step 1 - Solve 1 equation:
Step 2 - Replace it in the other equation:
You don't need to go on solving this one, but in case you want to
Step 3 - Solve the equation:
Step 4 - Replace the value in any equation:
The solution to question 5 is 11c+8.75(46-c)=470 and he has worked 30 hours as an office clerk and 16 as a cashier
I hope I've helped you, have a nice day.