Abaseball team had $1,000 to spend on supplies. the team spent $185 on a new bat. new
baseballs cost $4 each. the inequality 185 + 4b ≤ 1,000 can be used to determine the number
of new baseballs (b) that the team can purchase. which statement about the number of new
baseballs that can be purchased is true?

a. the team can purchase 204 new baseballs.
b. the minimum number of new baseballs that can be purchased is 185.
c. the maximum number of new baseballs that can be purchased is 185.
d. the team can purchase 185 new baseballs, but this number is neither the maximum nor the minimum.

D. The team can purchase 185 new baseballs, but this number is neither the maximum nor the minimum.

Explanation:

Inequalities

They are relations where variables and constants are compared by not using the equal sign. Common inequalities use the following signs

among others.

Solving a single inequality uses similar procedures as equations, but extra care must be taken when multiplying or dividing by negative numbers.

Being b the number of baseballs the team can buy, there is a restriction on the budget, expressed as

Subtracting 185 to both sides:

Solving for b

Or, equivalently

Analyzing each option we have

A. The maximum number of ball has been computed above and cannot be 204. This option is incorrect

B. The solution of the inequality does not say anything about the minimum mumber of baseballs to purchase, so this is not correct

C. As commented in the option A., the maximum number was determined to be 203.75, not 185

D. The team can purchase 185 new baseballs, but it's not in the boundary, it's just part of the solution. This is the correct option.

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