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$3.5c-1.5d \geq 50$ $\newline$ Esa's Pastries sells cupcakes for $\$3.50$ each and donuts for $\$1.50$ each. The given inequality represents the difference, in dollars, between cupcake sales and donut sales on a typical day based on $c$ , the number of cupcakes sold and $d$ , the number of donuts sold. If Esa sold $200$ donuts on a typical day, what is the minimum number of cupcakes she sold on that day? $\newline$ Choose $1$ answer: $\newline$ (A) $25$ $\newline$ (B) $50$ $\newline$ (C) $100$ $\newline$ (D) $350$

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One-step inequalities: word problems

Full solution

Q.

3.5c-1.5d \geq 50

\newline

Esa's Pastries sells cupcakes for

\$3.50

each and donuts for

\$1.50

each. The given inequality represents the difference, in dollars, between cupcake sales and donut sales on a typical day based on

c

, the number of cupcakes sold and

d

, the number of donuts sold. If Esa sold

200

donuts on a typical day, what is the minimum number of cupcakes she sold on that day?

\newline

Choose

1

answer:

\newline

(A)

25

\newline

(B)

50

\newline

(C)

100

\newline

(D)

350

Substitute donuts into inequality: Substitute the given number of donuts into the inequality. $\newline$ We are given that Esa sold $200$ donuts. Let's substitute $d = 200$ into the inequality $3.5c - 1.5d \geq 50$ . $\newline$ $3.5c - 1.5(200) \geq 50$
Perform multiplication: Perform the multiplication. $\newline$ Calculate the value of $1.5 \times 200$ . $\newline$ $3.5c - 300 \geq 50$
Add to isolate term with $c$ : Add $300$ to both sides to isolate the term with $c$ . We want to find the value of $c$ , so we need to get $c$ on one side of the inequality by itself. $3.5c - 300 + 300 \geq 50 + 300$ $3.5c \geq 350$
Divide to solve for $c$ : Divide both sides by $3.5$ to solve for $c$ . To find the value of $c$ , divide both sides of the inequality by $3.5$ . $c \geq \frac{350}{3.5}$
Perform division to find minimum cupcakes: Perform the division to find the minimum number of cupcakes. $\newline$ Calculate $350 / 3.5$ . $\newline$ $c \geq 100$

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Sean's justification:

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Is Issac's justification complete? If not, why?

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Issac's justification:

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(B) No, Issac didn't establish that

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Below is Bridget's attempt to write a formal justification for the fact that the equation

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\newline

Is Bridget's justification complete? If not, why?

\newline

Bridget's justification:

\newline

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\newline

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\newline

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(C) No, Bridget didn't establish that

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\newline

Ibrahim's justification:

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\newline

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(B) No, Ibrahim didn't establish that

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Below is Amrita's attempt to write a formal justification for the fact that the equation

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Is Amrita's justification complete?

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\newline

Amrita's justification:

\newline

Polynomial and trigonometric functions are differentiable and continuous at all points in their domain, and

[-1,4]

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(A) Yes, Amrita's justification is complete.

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(B) No, Amrita didn't establish that the average rate of change of

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(A) Yes, Omar's justification is complete.

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\newline

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\newline

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\newline

Lena's justification:

\newline

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\newline

So, according to the mean value theorem,

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1

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(B) No, Lena didn't establish that the average rate of change of

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(C) No, Lena didn't establish that

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Is Uriah's justification complete? If not, why?

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Uriah's justification:

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