Q3. - Algebra 2

Question

Determine which expression below represents the amount of change someone would receive from a $\mathrm{\backslash (}50$ bill if they purchased 2 children’s ticket at $\backslash )4.25$ each and 3 adult ticket at $\$7$ each at a movie theatre. Explain.

$\begin{array}{l}\text{a. }50-2\times 4.25+3\times 7\text{ b. }50-\left(2\times 4.25+3\times 7\right)\\ \text{c. }\left(50-2\times 4.25\right)+3\times 7\text{ d. }50-\left(2\times 4.25\right)+\left(3\times 7\right)\end{array}$

 

Step-by-Step Solution

Answer

Option b. $50-\left(2\times 4.25+3\times 7\right)$ is the correct expression.

Since, a person buys 2 children’s ticket at $\$4.25$  each and 3 adult ticket at  $\$7$ each

So, the sum of $2\times 4.25$ and $3\times 7$ is to be subtracted from 50 which is correctly mentioned in option b.

Step 1 - Explain meaning of statement

A person buys 2 children’s ticket at  $\$4.25$ each and 3 adult ticket at $\$7$  each

So, the add $2\times 4.25$ with  $3\times 7$

Then subtract the resultant from 50. 

Step 2 - Explain the expression a. 50 - 2 × 4 . 25 + 3 × 7

Multiply 2 with $4.25$ and 3 with 7

Then subtract $2\times 4.25$ from 50 and add $3\times 7$ in resultant term

Since, $3\times 7$ is not subtracted from 50 

Thus, option a. is incorrect

Step 3 - Explain the expression b. 50 - 2 × 4 . 25 + 3 × 7

Multiply 2 with $4.25$ and 3 with 7

Add $2\times 4.25$ with $3\times 7$

Then subtract resultant from 50 

Since, statements mentioned in step 1 satisfies

Thus, option b. is correct

Step 4 - Explain the expression c. 50 - 2 × 4 . 25 + 3 × 7

Multiply 2 with  $4.25$

Then subtract $2\times 4.25$ from 50 

Multiply 3 with 7 and add resultant term in it.

Since, $3\times 7$ is not subtracted from 50 

Thus, option c. is incorrect

Step 5 - Explain the expression d. 50 - 2 × 4 . 25 + 3 × 7

Multiply 2 with $4.25$ and 3 with 7

Then subtract $2\times 4.25$ from 50 and add $3\times 7$ in resultant term

Since, $3\times 7$ is not subtracted from 50 

Thus, option d. is incorrect