Q15. - Algebra 1

Question

Angelina needs to buy 12 pieces of candy to take to a meeting. She has $\mathrm{\backslash (}16$. Each chocolate bar costs $\mathrm{\backslash )}2$, and each lollipop costs $\mathrm{\$}1$. Determine how many of each she can buy.  

 

A 6 chocolate bars, 6 lollipops

B 4 chocolate bars, 8 lollipops

C 7 chocolate bars, 5 lollipops

D 3 chocolate bars, 9 lollipops

Step-by-Step Solution

Answer

The required option is represented by B.

Step 1. Form two equations by using the provided information and making some consideration after it number the obtained equations.

Make consideration that x represents the count associated with chocolates and y represents the count associated with lollipops. And the total count 12 is associated with the addition of count related to chocolates and lollipops. Use the obtained consideration and observation to form the first equation.

 

$x+y=12\mathrm{......}\left(1\right)$

 

Form the second equation by performing multiplication between the price associated with one chocolate and the count associated with the total purchased chocolates and do the same with the lollipop and make an equation by taking the addition of chocolate and lollipop equal to the total money.

 

$$\begin{gathered} 2x+1\cdot y=16 \\ 2x+y=16\mathrm{......}\left(2\right) \end{gathered}$$

Step 2. Perform subtraction of equation (1) from the equation (2) to get the value of x after it use the obtained value to get the value of y .

Perform subtraction of equation (1) from the equation (2) to extract the value of x. 

 

$$\begin{gathered} \left(2x+y\right)-\left(x+y\right)=16-12 \\ 2x+y-x-y=4 \\ x=4 \end{gathered}$$

 

Use the obtained value of x into equation (1) to get the value of y.

$$\begin{gathered} 4+y=12 \\ y=12-4 \\ y=8 \end{gathered}$$

Step 3. Write the conclusion.

The obtained value of x and y represents the required count that is 4 associated with chocolates and 8 associated with lollipops.

 

This count is completely matching with the option B.