SOLUTION: I need help I have to question I cant figure up and I keep coming up with 2 diffrent answers 1. The sum of two numbers is 12. Three times the smaller number increased by the lar

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Question 245792: I need help I have to question I cant figure up and I keep coming up with 2 diffrent answers
1. The sum of two numbers is 12. Three times the smaller number increased by the larger number is 20. find the numbers.
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.
Thanks
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
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