Part I. Use two variables and two equations to set 
up each problem. Do not solve. 

You have to learn things like
"Twice" means "two times"
"Sum" means "what you get when you add".
"Is" means "equals".
"Difference" means "what you get when you subtract".


1. One integer is twice another 

y = 2x

and their sum is 96.  

x + y = 96


2. The sum of two integers is 38.  

x + y = 38

and their difference is 12.

x - y = 12

3. Three times one integer plus another integer is 29.

3x + y = 29

If the first integer plus twice the
second is 18. 

x + 2y = 18


4. Twice one integer plus another integer is 21.

2x + y = 21 

If the first integer plus 3 times the 
second is 33.

x + 3y = 33

Part II. Use two variables and two equations for 
each problem. Solve the systems by any method you 
choose, and write the answer in the appropriate form. 

5. A rancher raises five times as many cows as horses.

   C = 5H 

 If he has 168 animals, 

   C + H = 168

Substitute 5H for C in C + H = 165

  5H + H = 168
      6H = 168
       H = 168/6 = 31 horses

C = 5H = 5(31) = 155 cows.


6. A landscaper used 100 pounds of grass seed 

     B + R = 100

containing twice as much bluegrass
as rye. 

     B = 2R

Substitute 2R for B in B + R = 100

    2R + R = 100
        3R = 100
         R =  = 33 

B = 2R = 2(33) = 66

He added 15 more pounds of bluegrass 

66+15 = 81 pound of bluegrass.

7. A youth group with 26 members is going skiing. 
Each of the five chaperones will drive a van or 
a sedan. 

 V +  S =  5

The vans can seat seven people, and the sedans can seat 
five people. 

7V + 5S = 31

Solve the first for S.  S = 5 - V
Substitute in 7V + 5S = 31

7V + 5(5 - V) = 31
 7V + 25 - 5V = 31
      2V + 25 = 31
           2V = 31 - 25
           2V = 6
            V = 6/2 = 3

S = 5 - V = 5 - 3 = 2
 
2 sedans, 3 vans.  


8. In a mayoral election, the incumbent received 
25% more votes than the opponent.

("O" looks too much like zero, so I'll use the 
letter "P" for "OPPONENT")

I = P + .25P
or
I = 1.00P + .25P
or
I = 1.25P

Altogether, 5175 votes were cast for the two 
candidates.

I + P = 5175

Substitute 1.25P for I in I + P = 5175

    1.25P + P = 5175
1.25P + 1.00P = 5175
        2.25P = 5175
            P = 5175/2.25
            P = 2300

I = 1.25P = 1.25(2300) = 2875

So the ncumbent mayor received 2875 votes 
and the opponent received 2300

9. Macha knows that they used 295 cups that night.

   H + C = 295

>>...hot chocolate sells for $0.75 and coffee sells 
for $0.50...<<

>>...they sold $200 worth of hot drinks...<<

 0.75H + 0.50C = 200

You solve that by yourself!

Answer: H = 210 cups of hot chocolate, C = 85 cups of coffee. 

Edwin