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Ivan had saved
$500 from his summer job. He will need
$75 per month when he returns to school in the fall, but wants to keep at least
$50 in reserve. Which of the following inequalities best describes the number of months,
m, Ivan can use his funds, assuming there are no other additions to or withdrawals from his savings?
Choose 1 answer:
(A)
500-75 m < 50
(B)
500+75 m < 50
(C)
500-75 m >= 50
(D)
500+75 m >= 50

Ivan had saved $\$ 500$ from his summer job. He will need $\$ 75$ per month when he returns to school in the fall, but wants to keep at least $\$ 50$ in reserve. Which of the following inequalities best describes the number of months, $m$ , Ivan can use his funds, assuming there are no other additions to or withdrawals from his savings? $\newline$ Choose $1$ answer: $\newline$ (A) 500-75 m<50 $\newline$ (B) 500+75 m<50 $\newline$ (C) $500-75 m \geq 50$ $\newline$ (D) $500+75 m \geq 50$

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Write a linear inequality: word problems

Full solution

Q. Ivan had saved

\$ 500

from his summer job. He will need

\$ 75

per month when he returns to school in the fall, but wants to keep at least

\$ 50

in reserve. Which of the following inequalities best describes the number of months,

m

, Ivan can use his funds, assuming there are no other additions to or withdrawals from his savings?

\newline

Choose

1

answer:

\newline

(A)

500-75 m<50

\newline

(B)

500+75 m<50

\newline

(C)

500-75 m \geq 50

\newline

(D)

500+75 m \geq 50

Determine Initial Amount: Determine the initial amount of money Ivan has and the amount he wants to keep in reserve. Ivan has $\$500$ and wants to keep at least $\$50$ in reserve.
Calculate Remaining Amount: Calculate the amount Ivan can use after keeping the reserve. Ivan can use $\$500 - \$50 = \$450$ for his monthly expenses.
Find Monthly Expense: Determine the monthly expense. Ivan needs $\$75$ per month when he returns to school.
Set Up Inequality: Set up the inequality to represent the situation. The amount Ivan can use must be greater than or equal to the total expenses over $m$ months. The inequality is $\$450 \geq \$75m$ , which simplifies to $\$500 - \$75m \geq \$50$ .
Choose Correct Inequality: Choose the correct inequality from the given options that matches the one we found in Step $4$ . The correct inequality is (C) $500 - 75m \geq 50$ .

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