Question 379·Easy·Math

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In a recent survey of 800 adults, 560 said they preferred coffee over tea. What percentage of the surveyed adults preferred coffee?

A survey asking “what percentage” uses a part-whole relationship: compare one group with everyone surveyed. The whole is all surveyed adults, and the part is the group with the named preference. Write “unknown percent of whole = part,” then use a Desmos regression to find the percent. Dividing by a smaller group answers a different question.

Hints

Hint 1
The whole is the group counted as $100\%$ . The question asks for a percentage of everyone surveyed, not just the adults who preferred coffee. Which count represents everyone?
Hint 2
The part is the group whose share you want. Put the unknown percent of the whole equal to that group's count. In Desmos, a regression finds the unknown when you use $x_1$ and $\sim$ .

Step-by-step

Match the coffee group to the whole survey
Step 1
Write the percent relationship
The whole is all $800$ surveyed adults, and the part is the $560$ who preferred coffee. Let $x$ be the number in the requested percent. A percent compares the part with the whole, so use all surveyed adults after “of”:
$x\%\text{ of }800=560.$
Step 2
Find and interpret the unknown percent
Type $x_1\%\operatorname{of}800\sim560$ in Desmos. Replace $x$ with $x_1$ and $=$ with $\sim$ to make a regression that finds the unknown. Under PARAMETERS, Desmos shows $x_1=70$ . That's the number before the percent sign, so $70\%$ of the surveyed adults preferred coffee. Choice C.

Question 379·Easy·Math

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