Question

4 tyler filled a small jar with quarters and dimes and donated it to his schools charity club. the club member receiving the jar asked, \do you happen to know how much is in the jar?\ tyler said, \i know its at least $8.50, but i dont know the exact amount.\ a. write an inequality to represent the relationship between the number of dimes, d, the number of quarters, q, and the dollar amount of the money in the jar. b. graph the solution set to the inequality and explain what a solution means in this situation. c. suppose tyler knew there were 25 dimes in the jar. write an inequality that represents how many quarters could be in the jar. 5 from unit 4, lesson 3 andre is solving the inequality ( 14x + 3 leq 8x + 3 ). he first solves a related equation. ( 14x + 3 = 8x + 3 ) ( 14x = 8x ) ( 8 = 14 ) this seems strange to andre. he thinks he probably made a mistake. what was his mistake?

Explanation:

Step1: Analyze the value of dimes and quarters

A dime is worth $0.1$ dollars and a quarter is worth $0.25$ dollars. The total amount of money in the jar is the sum of the value of dimes and quarters.

Step2: Write the inequality for part a

The total amount is $0.1d + 0.25q$. Since the amount is at least $8.50$, the inequality is $0.1d+0.25q\geq8.50$.

Step3: Analyze Andre's mistake

Starting with $14x + 3=8x + 3$. Subtract $3$ from both sides: $14x=8x$. Then subtract $8x$ from both sides: $14x - 8x=8x-8x$, which gives $6x = 0$, so $x = 0$. Andre made a mistake when he went from $14x=8x$ to $8 = 14$. He should have subtracted $8x$ from both sides instead of dividing incorrectly.

Step4: Write the inequality for part c

If $d = 25$, substitute into the inequality from part a. $0.1\times25+0.25q\geq8.50$. Simplify: $2.5+0.25q\geq8.50$.

Answer:

a. $0.1d + 0.25q\geq8.50$
c. $2.5+0.25q\geq8.50$
Andre's mistake: When solving $14x=8x$, he should subtract $8x$ from both sides ($6x = 0$, $x = 0$) instead of getting $8 = 14$.