Laurie buys milk and bread for his family on the way
home from school each day, paying with a $10 note. If he buys three cartons of milk and two loaves of bread, he receives 5 cents in change. If he buys two cartons of milk and one loaf of bread, he receives $4.15 in change. How much does each item cost?
3m+2b = 995
2m+b = 585
Now just solve for m and b (in cents)
Thanks again Steve :>
Yup, got the answer, thanks!
To find out the cost of each item, we can use a system of equations. Let's assume the cost of a carton of milk is x dollars and the cost of a loaf of bread is y dollars.
From the given information:
Scenario 1:
- Laurie bought 3 cartons of milk and 2 loaves of bread, and received 5 cents in change.
- The total cost of the milk is 3x dollars and the total cost of the bread is 2y dollars.
- Since Laurie paid with a $10 note and received 5 cents in change, the equation becomes: 10 = 3x + 2y + 0.05.
Scenario 2:
- Laurie bought 2 cartons of milk and 1 loaf of bread, and received $4.15 in change.
- The total cost of the milk is 2x dollars and the total cost of the bread is y dollars.
- Again, using the payment information, the equation becomes: 10 = 2x + y + 4.15.
We now have a system of two equations to solve:
Equation 1: 10 = 3x + 2y + 0.05
Equation 2: 10 = 2x + y + 4.15
To solve this system, we can use either substitution or elimination method. Let's use the elimination method.
Subtract Equation 2 from Equation 1 to eliminate y:
(10 - 3x - 2y - 0.05) - (10 - 2x - y - 4.15) = 0
Simplifying this equation gives us:
-3x - 2y - 0.05 + 2x + y + 4.15 = 0
-x - y + 4.1 = 0
-x - y = -4.1
Now, let's multiply Equation 2 by -2 and add it to the above equation to eliminate x:
-2(10 = 2x + y + 4.15)
-20 = -4x - 2y - 8.3
Simplifying this equation gives us:
-4x - 2y - 8.3 + x + y = -4.1
-3x - y = 4.2
Now we have another equation:
-x - y = -4.1
-3x - y = 4.2
Simplifying the two equations, we have:
x + y = 4.1
-3x - y = 4.2
Solving the system of equations by elimination or substitution, we find that x = 2.15 and y = 1.95.
Therefore, a carton of milk costs $2.15 and a loaf of bread costs $1.95.