Foam fingers sold for $5. Spirit bracelets for $4. You sold 40 more foam fingers than bracelets and earned $965. Write a system of equations to describe this situation.
Solve this system using as least 2 different methods. Explain each method.
Let F and B be the two variables: the number of each that were sold.
Your sytemn of equations is
F - B = 40
5F + 4B = 965
Now use what you have learned to solve them. Try substitution first.
To write a system of equations to describe this situation, we can let x represent the number of spirit bracelets sold and y represent the number of foam fingers sold.
The first equation represents the cost of the items sold:
4x + 5y = 965
The second equation represents the relationship between the number of bracelets and foam fingers sold:
y = x + 40
Now, let's solve this system of equations using two different methods: substitution and elimination.
Method 1: Substitution
We can solve this system by substituting the second equation into the first equation.
Substitute y in terms of x from the second equation into the first equation:
4x + 5(x + 40) = 965
Simplify the equation:
4x + 5x + 200 = 965
9x + 200 = 965
9x = 765
x = 85
Substitute the value of x back into the second equation:
y = 85 + 40
y = 125
Therefore, the solution is x = 85 and y = 125.
Method 2: Elimination
We can solve using elimination by multiplying the second equation by -5 to eliminate the y variable.
Multiply the second equation by -5:
-5(y) = -5(x + 40)
-5y = -5x - 200
Now, add the first equation and the rewritten second equation:
4x + 5y + (-5x) + (-5y) = 965 + (-200)
-x = -235
x = 235
Substitute the value of x back into the second equation:
y = x + 40
y = 235 + 40
y = 275
Therefore, the solution is x = 235 and y = 275.
In both methods, we obtained the same solution x = 235 and y = 275, which means that 235 spirit bracelets and 275 foam fingers were sold.