Anita and Maria went to the candy store. Maria bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70. Anita bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60. Determine the cost of 1 piece of bubble gum.
To determine the cost of 1 piece of bubble gum, we can use algebraic reasoning.
Let's assign variables to the unknowns:
Let's call the cost of 1 piece of fudge "f" and the cost of 1 piece of bubble gum "b".
According to the given information:
Maria bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70.
This equation can be written as:
5f + 3b = 5.70 .......(Equation 1)
Anita bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60.
This equation can be written as:
2f + 10b = 3.60 .......(Equation 2)
We now have a system of two equations with two unknowns:
5f + 3b = 5.70 .......(Equation 1)
2f + 10b = 3.60 .......(Equation 2)
To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method:
Multiply Equation 1 by 10 and Equation 2 by 3 to eliminate the variable "f".
10*(5f + 3b) = 10*5.70 => 50f + 30b = 57 .......(Equation 3)
3*(2f + 10b) = 3*3.60 => 6f + 30b = 10.80 .......(Equation 4)
Now, subtract Equation 4 from Equation 3 to eliminate "b":
(50f + 30b) - (6f + 30b) = 57 - 10.80
44f + 0b = 46.20
44f = 46.20
f = 46.20 / 44
f ≈ 1.05
Now we have the price of 1 piece of fudge, which is approximately $1.05. We can substitute this value back into Equation 1 or Equation 2 to find the price of 1 piece of bubble gum.
Substituting f = 1.05 into Equation 1:
5(1.05) + 3b = 5.70
5.25 + 3b = 5.70
3b = 5.70 - 5.25
3b = 0.45
b = 0.45 / 3
b ≈ 0.15
Therefore, the cost of 1 piece of bubble gum is approximately $0.15.