Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

In order to fulfill a local school's request for \(x\) cakes, \(B\) parents agreed to each bake an equal number of cakes. If \(p\) of the parents did not bake any cakes, which of the following represents the additional number of cakes that each of the other parents had to bake in order for the school's request for \(x\) cakes to be fulfilled? A. $$\frac{p x}{B}$$ B. $$\frac{p x}{B(B-p)}$$ C. $$\frac{x}{B-p}$$ D. $$\frac{p}{R_{m} r}$$ E. $$\frac{p}{B(B-p)}$$

Short Answer

Expert verified
\frac{p x}{B(B - p)}

Step by step solution

01

Determine initial number of cakes per parent

Initially, there are B parents who were supposed to bake a total of x cakes. Each parent would have baked \(\frac{x}{B}\) cakes.
02

Determine the number of remaining parents

Since p parents did not bake any cakes, there are now \(B - p\) parents baking the cakes.
03

Total number of cakes needed to be baked by remaining parents

The total number of cakes to be baked remains x.!
04

Determine the new number of cakes each of the remaining parents needs to bake

Since \(B - p\) parents are baking x cakes, each of these remaining parents needs to bake \(\frac{x}{B - p}\) cakes.
05

Determine the additional number of cakes each remaining parent has to bake

Initially, each of the B parents was baking \( \frac{x}{B} \) cakes. Now, each remaining parent has to bake \( \frac{x}{B - p} \) cakes. The additional number of cakes each remaining parent has to bake is: \(\frac{x}{B - p} - \frac{x}{B}\). This can be simplified to \( \frac{p x}{B(B - p)} \).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

algebraic expressions
Understanding algebraic expressions is crucial for solving word problems, especially in exams like the GMAT. In this exercise, we deal with expressions to determine how many cakes each parent must bake. An algebraic expression represents numbers and variables along with arithmetic operations. Here, the expressions \( \frac{x}{B} \) and \( \frac{x}{B - p} \) show us how many cakes each parent would bake initially and after some parents didn't bake any cakes. By analyzing these expressions, we calculate the difference to find out the additional number of cakes each remaining parent needs to bake to meet the school's request.
division of labor
The division of labor concept helps in distributing tasks equally among all participants. It's an essential strategy in teamwork to ensure efficiency and productivity. In our exercise, the school requested a total of \( x \) cakes, and initially, \( B \) parents were to bake them. When \( p \) parents didn't bake, the remaining \( B - p \) parents divided the task among themselves. This led to each remaining parent having to bake more cakes than originally planned. The aim is to understand how the workload shifts when some team members can't contribute.
logical reasoning
Logical reasoning is about understanding and applying steps and rules to solve problems. It's especially useful in word problems like the one in the exercise. We start by finding how many cakes each parent initially needed to bake, then assess the situation after some parents can't bake. By using logical thinking, we determine the new number of cakes each remaining parent needs to bake. The logical steps lead us to find that the additional cakes each remaining parent needs to bake is represented by \( \frac{p x}{B(B - p)} \). This clear and systematic approach helps break down and solve complex problems.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A teacher grades students' tests by subtracting twice the number of incorrect responses from the number of correct responses. If Student A answers each of the 100 questions on her test and receives a score of \(73,\) how many questions did Student A answer correctly? A 55 B 60 C 73 D 82 E 91

The positive difference between Sam and Lucy's ages is \(a\), and the sum of their ages is \(z\). If Lucy is older than Sam, then which of the following represents Lucy's age? A. $$\frac{z-a}{2}$$ B. $$a-\frac{z}{2}$$ C. $$2 a+z$$ D. $$\frac{z+a}{2}$$ E. $$\frac{a-z}{2}$$

John spent 40 percent of his earnings last month on rent and 30 percent less than what he spent on rent to purchase a new dishwasher. What percent of last month's earnings did John have left over? A. $$30 \%$$ B. $$32 \%$$ C. $$45 \%$$ D. $$68 \%$$ E. $$70 \%$$

Each writer for the local newspaper is paid as follows: \(a\) dollars for each of the first \(n\) stories each month, and \(a+b\) dollars for each story thereafter, where \(a>b\). How many more dollars will a writer who submits \(n+a\) stories in a month earn than a writer who submits \(n+b\) stories? A. $$(a-b)(a+b+n)$$ B. $$a-b$$ C. $$a^{2}-b^{2}$$ D. $$n(a-b)$$ E. $$a n+b n-a n$$

A machine manufactures notebooks in a series of five colors: red, blue, black, white, and yellow. After producing a notebook of one color from that series, it produces a notebook of the next color. Once five are produced, the machine repeats the same pattern. If the machine began a day producing a red notebook and completed the day by producing a black notebook, how many notebooks could have been produced that day? A. $$27$$ B. $$34$$ C. $$50$$ D. $$61$$ E. $$78$$

See all solutions

Recommended explanations on English Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free