Math question to answer

Question

Chase and Sara went to the candy store. Chase bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70. Sara bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60. How much would it cost for one piece of fudge and one piece of bubble gum? Write your answer as an ordered pair. *

 

Answer 1

The first step is to write the word problem in the form of an equation, in this instance 2 equations. If we use the variable f for the cost of fudge and b for the cost of bubble gum, then we can write the first set of information as:

5f + 3b = $5.70

and the second set as:

2f + 10b = $3.60

For the final answer we need to find f + b, so we need to define one variable in terms of the other by isolating a single variable on one side of the equation. In this case we'll subtract the second equation from the first to solve for f.

5f + 3b = $5.70

-(2f + 10b = $3.60)

3f - 7b = $2.10

To get the equation for f, add 7b to both sides of the equation

3f - 7b + 7b = $2.10 + 7b

3f = $2.10 + 7b

And divide by 3

3f/3 = ($2.10 + 7b)/3

So f = $0.70 + (7/3)b

or f = (7/3)b + $0.70

Now we can substitute the equation for f into either original equation to solve for b

5f + 3b = $5.70

5[(7/3)b + $0.70] + 3b = $5.70

(35/3)b + $3.50 + 3b = $5.70

Isolate the variables on one side by subtracting $3.50 from both sides of the equation

$3.50 - $3.50 + (35/3)b + 3b = $5.70 - $3.50

(35/3)b + 3b = $2.20

Multiply both sides by 3 to eliminate fractions

3[(35/3)b + 3b] = 3($2.20)

35b + 9b = $6.60

Combine like variables

44b = $6.60

Divide both sides of the equation by 44 to get the value for b

44b/44 = $6.60/44

b= $0.15

Now use the value of b to calculate the value of f. I will use both equations to check the answer.

5f + 3b = $5.70

5f + 3($0.15) = $5.70

5f + $0.45 = $5.70

5f + $0.45 - $0.45 = $5.70 - $0.45

5f = $5.25

5f/5 = $5.25/5

f= $1.05

2f + 10b = $3.60

2f + 10($0.15) = $3.60

2f + $1.50 = $3.60

2f + $1.50 - $1.50 = $3.60 - $1.50

2f = $2.10

2f/2 = $2.10/2

f = $1.05

Since both answers are the same it confirms that the correct answer for f is $1.05 and b is $0.15

So for one piece of fudge and one piece of bubble gum the equation would be f + b = total, and with the known values being used instead of variables it is $1.05 + $0.15 = $1.20

To write it as an ordered pair in the form of (x,y) or in this case (f,b) the final answer would be

($1.05, $0.15)