Question

A. Morgan is saving to buy a bicycle that costs $135. She has saved $98 and wants to know how much more money she needs to buy the bicycle. The equation 135 = x + 98 models this situation, where x represents the additional amount of money Morgan needs to buy the bicycle.When substituting for x, which value(s), if any, from the set {0, 37, 98, 135, 233} will make the equation true? Explain what this means in terms of the amount of money needed and the cost of the bicycle.B. Morgan considered buying the $135 bicycle, but then she decided to shop for a different bicycle. She knows the other bicycle she likes will cost more than $150. This situation can be modeled by the following inequality. x + 98 >150 Which values, if any from -250 to 250 will make the inequality true? If more than one value makes the inequality true, identify the least and greatest values that make the inequality true. Explain what this means in terms of the amount of money needed and the cost of the bicycle.

Answer 1

A. Given the equation

$135=x+98$

Solve for x:

$\begin{gathered} 135-98=x+98-98 \\ x=37 \end{gathered}$

Answer: 37 is the only value in the set that makes the equation true

Explain

This means that Morgan will need exactly $37 more to buy the bicycle

B. The inequality is:

$x+98>150$

Then solve for x:

$\begin{gathered} x+98-98>150-98 \\ x>52 \end{gathered}$

This means that values greater than 52 satisfy the inequality, so:

the smallest value is 53 and the largest is 250.

Answer: