Question 245792
1. The sum of two numbers is 12. Three times the smaller number increased by the larger number is 20. find the numbers.
.
Let x = smaller number
and y = larger number
then
From: "The sum of two numbers is 12" we get:
x + y = 12
From: "Three times the smaller number increased by the larger number is 20" we get
3x + y = 20
.
x + y = 12   (equation 1)
3x + y = 20  (equation 2)
.
Multiply both sides of equation 1 by -1:
-x - y = -12
3x + y = 20
.
Combine (add) both equations together:
-x - y = -12
3x + y = 20
-------------
2x     = 8
x = 4
.
Substitute the above back into equation 1 and solve for y:
x + y = 12
4 + y = 12
y = 8
.
Solution: your two numbers are 4 and 8
.
2. A deli charges $3.80 for a breakfast of three eggs and four strips of bacon. The charge is $2.75 for two eggs and trhee strips of bacon. find the cost of each egg and the cost of each strip of bacon. 
.
Let e = cost of eggs
and b = cost of bacon
then
From: "A deli charges $3.80 for a breakfast of three eggs and four strips of bacon."
3.80 = 4e + 4b
0.95 =  e +  b (equation 1)
From: "The charge is $2.75 for two eggs and three strips of bacon."
2.75 = 2e + 3b (equation 2)
.
0.95 =  e +  b 
2.75 = 2e + 3b 

Multiplying the first equation by -2:
-1.90 = -2e - 2b
 2.75 =  2e + 3b 
.
Adding the two equations together:
-1.90 = -2e - 2b
 2.75 =  2e + 3b 
-----------------
0.85 = b 
.
Substitute the above into equation 1:
0.95 =  e +  b
0.95 =  e +  0.85
0.10 = e
.
Solution:
one egg costs 10 cents
one strip of bacon costs 85 cents