155k views
0 votes
System of Equations

8th grade
30 points

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?

User Noio
by
8.5k points

1 Answer

3 votes
Let x represent the cost of liters of milk
y represent the cost of bread
Next, Bhavik bought 3 liters of milk and 5 loaves of bread for a total of $11 means that:
3x+5y=11
Multiply both side by 4
3x(4)+5y(4)=11(4)
12x+20y=44
Then, he bought 4 liters of milk and 4 loaves of bread at the same prices, for a total of $10 also means that:
4x+4y=10
Multiply both side by 3
4x(3)+4y(3)=10(3)
12x+12y=30

12x+20y=44
12x+12y=30
Use substitute property
12x+20y=44
-
12x+12y=30
=
8y=14
Divided both side by
8y/8=14/8
y=$1.75/ loaf of bread
3x+5y=11
Substitute y with 1.75
3x+5(1.75)=11
3x+8.75=11
Subtract 8.75 to each side
3x+8.75-8.75=11-8.75
3x=2.25
Divided both side by 3
3x/3=2.25/3
x=$0.75/liter of milk
Check:
3x+5y=11
Substitute x with 0.75 and y with 1.75
3(0.75)+5(1.75)=11
2.25+8.75=11
11=11

4x+4y=10
Substitute x with 0.75 and y with 1.75
4(0.75)+4(1.75)=10
3+7=10
10=10. As a result, a liter of milk cost $0.75 and the cost of bread cost $1.75. Hope it help!
User Mohammad Abumazen
by
7.6k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories