Math  /  Algebra

QuestionFor each context, define variables, write a linear system modeling the situation, solve it, and answer the questions.
3. At Culver's, Fern purchased 4 Butterburgers and one small soda for a total cost of $12.85\$ 12.85. The price of the soda was $1.10\$ 1.10 less than the price of a Butterburger. What is the price of a Butterburger? What is the price of a small soda?

Studdy Solution

STEP 1

What is this asking? We need to find the price of a Butterburger and a soda at Culver's, knowing the total cost of Fern's order and that the soda is cheaper than the burger. Watch out! Make sure to match the number of burgers and sodas to the prices when setting up the equation.
Don't mix them up!

STEP 2

1. Define variables and set up the system of equations.
2. Solve for the price of a Butterburger.
3. Solve for the price of a soda.

STEP 3

Let bb be the price of a Butterburger in $\$ and ss be the price of a small soda in $\$.

STEP 4

Fern bought 4 Butterburgers and 1 soda for a total of $12.85\$12.85.
So, our first equation is: 4b+s=12.854b + s = 12.85

STEP 5

We also know the soda price is $1.10\$1.10 *less* than the Butterburger price.
This translates to: s=b1.10s = b - 1.10

STEP 6

We can **substitute** the second equation into the first equation to eliminate ss: 4b+(b1.10)=12.854b + (b - 1.10) = 12.85

STEP 7

Now, **combine** the bb terms: 5b1.10=12.855b - 1.10 = 12.85

STEP 8

**Add** 1.101.10 to both sides of the equation to **isolate** the term with bb: 5b=12.85+1.105b = 12.85 + 1.10 5b=13.955b = 13.95

STEP 9

Finally, **divide** both sides by 55 to find the price of a Butterburger: b=13.955b = \frac{13.95}{5} b=2.79b = 2.79So, the price of one Butterburger is $2.79\$2.79.

STEP 10

Now that we know b=2.79b = 2.79, we can **substitute** this value back into the equation s=b1.10s = b - 1.10 to find the price of the soda: s=2.791.10s = 2.79 - 1.10

STEP 11

s=1.69s = 1.69 Therefore, the price of a small soda is $1.69\$1.69.

STEP 12

A Butterburger costs $2.79\$2.79 and a small soda costs $1.69\$1.69.

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