Answer:
System of equations: [tex]\left \{ {{3b+5s=2.31} \atop {5b+3s=3.05}} \right.[/tex]
A bar soap costs $0.52 and a sponge costs $0.15
Step-by-step explanation:
Let be "x" the cost in dollars of a bar of soap and "y" the cost in dollars of a sponge.
Based on the information given in the exercise, you can set up the following system of equations:
[tex]\left \{ {{3x+5y=2.31} \atop {5x+3y=3.05}} \right.[/tex]
You can use the Elmination method to solve the system of equations:
1. Multiply the first equation by -3 and the second one by 5.
2. Add the equations.
3. Solve for "x".
Then:
[tex]\left \{ {{-9x-15y=-6.93} \atop {25x+15y=15.25}} \right\\........................\\16x=8.32\\\\x=0.52[/tex]
4. Substitute the value of "x" into any original equation and solve for "y":
[tex]3(0.52)+5y=2.31\\\\5y=2.31-1.56\\\\5y=0.75\\\\y=0.15[/tex]
