Question

lets solve the word problem below by creating and solving a system of equations by elimination. kayla sells candy bars and cans of soda. she charges $3 for candy bars and $1 for soda. yesterday she sold 70 items altogether and earned $100. how much candy did she sell? how much soda? solution: she sold ____ candy bars and ____ cans of soda!

Explanation:

Step1: Define variables

Let $x$ be the number of candy - bars and $y$ be the number of cans of soda.
We have two equations based on the given information:
Equation 1 (total number of items): $x + y=70$, which can be rewritten as $y = 70 - x$.
Equation 2 (total money earned): $3x + y=100$.

Step2: Substitute $y$ in the second equation

Substitute $y = 70 - x$ into $3x + y=100$.
We get $3x+(70 - x)=100$.

Step3: Simplify the equation

Expand the left - hand side: $3x+70 - x=100$.
Combine like terms: $2x+70 = 100$.

Step4: Solve for $x$

Subtract 70 from both sides: $2x=100 - 70$, so $2x = 30$.
Divide both sides by 2: $x=\frac{30}{2}=15$.

Step5: Solve for $y$

Substitute $x = 15$ into $y = 70 - x$.
$y=70 - 15=55$.

Answer:

She sold 15 candy bars and 55 cans of soda.