Question

each equation below is followed by several stories.
select all of the stories that can be represented by the equation.
if none of the stories can be represented, select
one of the above\.

(a) select the stories represented by this equation.

$18x - 45 = 117$

□today, charmaine used $45 of her savings to buy a bike. she has been putting $18 into her savings each week for x weeks. after buying the bike, she now has $117 left in her savings.

□charmaine is saving money and already has $45 saved. she is going to save an additional x dollars each week for 18 weeks. this will give her enough money for a bike that costs $117.

□charmaine is saving money and already has $45 saved. she is going to save an additional $18 each week for x weeks. this will give her enough money for a bike that costs $117.

□today, charmaine used $45 of her savings to buy a bike. she has been putting x dollars into her savings each week for 18 weeks. after buying the bike, she now has $117 left in her savings.

□none of the above

(b) select the stories represented by this equation.

$36x + 18 = 270$

□a printing company charges x dollars per banner. there is also a one - time setup fee of $18. chau printed 36 banners. he paid a total of $270 including the setup fee.

□a printing company charges x dollars per banner. there is also a one - time setup fee of $36. chau printed 18 banners. he paid a total of $270 including the setup fee.

□a printing company charges $18 per banner. there is also a one - time setup fee of $36. chau printed x banners. he paid a total of $270 including the setup fee.

□a printing company charges $36 per banner. there is also a one - time setup fee of $18. chau printed x banners. he paid a total of $270 including the setup fee.

□none of the above

Explanation:

Step1: Analyze equation (a) matches

Equation: $18x - 45 = 117$

• Story 1: Total savings = $18x$, subtract $45$ spent, left with $117$. Matches: $18x - 45 = 117$.
• Story 2: Equation would be $45 + 18x = 117$. Does not match.
• Story 3: Equation would be $45 + 18x = 117$. Does not match.
• Story 4: Equation would be $18x - 45 = 117$ but $x$ is weekly amount, not weeks. Does not match.

Step2: Analyze equation (b) matches

Equation: $36x + 18 = 270$

• Story 1: Equation would be $36x + 18 = 270$. Matches.
• Story 2: Equation would be $18x + 36 = 270$. Does not match.
• Story 3: Equation would be $36 + 18x = 270$. Does not match.
• Story 4: Equation would be $36x + 18 = 270$. Matches.

Answer:

(a) Today, Charmaine used $45 of her savings to buy a bike. She has been putting $18 into her savings each week for x weeks. After buying the bike, she now has $117 left in her savings.
(b) A printing company charges x dollars per banner. There is also a one-time setup fee of $18. Chau printed 36 banners. He paid a total of $270 including the setup fee.
(b) A printing company charges $36 per banner. There is also a one-time setup fee of $18. Chau printed x banners. He paid a total of $270 including the setup fee.