Bhavik bought 3 liters of milk and 5 loaves of bread for a total of $11. A month later, he bought 4 liters of milk and 4 loaves of bread at the same prices, for a total of $10. How much does a liter of milk cost, and how much does a loaf of bread cost?
Answers
Answer:
Let m = cost of a liter of milk
Let b = cost of a loaf of bread
Bhavik bought 3 liters of milk and 5 loaves of bread
for a total of $11 so:
3m + 5b = 11
Prices didn't change and he bought 4 liters of milk
and 4 loaves of bread for $10 a month later so:
4m + 4b = 10
We have two equations:
3m + 5b = 11 equation 1
4m + 4b = 10 equation 2
To eliminate a variable we want the coefficients to add to zero.
Multiply equation 1 by 4 and equation 2 by -3. This will give us
12m in the first equation and -12m in the 2nd equation so that
we can then add the two and eliminate the m variable, thus
allowing us to solve for b.
12m + 20b = 44 4(equation 1)
-12m - 12b = -30 -3(equation 2)
--------------------
0m + 8b = 14 sum of the equations
8b = 14
b = 14/8
b = 1.75
A loaf of bread costs $1.75
Substitute that value into one of the original 2 equations
and solve for m
4m + 4b = 10
4m + 4(1.75) = 10
4m + 7 = 10
4m = 3
m = 3/4
m = .75
A liter of milk costs $.75
A loaf of bread costs $1.75
Check answer:
3m + 5b = 11
3(.75) + 5(1.75) = 11
2.25 + 8.75 = 11
11 = 11
4m + 4b = 10
4(.75) + 4(1.75)=10
3 + 7 = 10
10 = 10
Our answer fits the parameters of the given information.