₦airaland Forum

QUESTION 11a

Find the equation of the line that passes through the origin and the point of intersection of the lines x + 2y = 7 and
x - y = 4

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A company installs solar panels in its premises to reduce its electricity cost. The monthly savings on electricity in $, is modelled by S = 200 + 50x - 2x² , where x is the number of months after installation. Find the time that the savings on electricity stop increasing and the maximum savings?

solution

Maximum/minimum value of a quadratic function
1. Identify the type of function — Notice that S = 200 + 50x − 2x² is a quadratic expression in x, with the coefficient of x² being negative (−2). By definition, a quadratic with a negative leading coefficient has a graph that opens downward, so it possesses a maximum value rather than a minimum. This maximum point is exactly where the savings stop increasing and begin to decrease.

2. Locate the turning point — For any quadratic S = ax² + bx + c, the turning point occurs at x = −b/(2a). Here we identify a = −2 and b = 50, since the expression is written as S = −2x² + 50x + 200. It follows that x = −50/(2×−2) = −50/−4 = 12.5.

3. Interpret the value of x — Since x represents the number of months after installation, we conclude that the savings stop increasing 12.5 months after the panels are installed — this is the instant the monthly saving reaches its peak before beginning to decline.

4. Find the maximum saving — To find the maximum value of S, we substitute x = 12.5 back into the original equation, since the maximum saving occurs precisely at the turning point. This gives us S = 200 + 50(12.5) − 2(12.5)².

5. Simplify the arithmetic — We compute each term carefully: 50 × 12.5 = 625, and 12.5² = 156.25, so 2 × 156.25 = 312.5. Hence S = 200 + 625 − 312.5 = 512.5.

6. State the conclusion — We therefore conclude that the savings stop increasing at x = 12.5 months, at which point the maximum monthly saving is $512.50.

Answer: The savings stop increasing after 12.5 months, with a maximum monthly saving of $512.50.

EXAMINERS WORKINGS

S = 200 + 50x − 2x² = −2x² + 50x + 200
a = −2, b = 50, c = 200
Turning point: x = −b/(2a) [M1]
x = −50/(2×−2) = −50/−4 = 12.5 [A1]
∴ savings stop increasing at x = 12.5 months
S(max) = 200 + 50(12.5) − 2(12.5)² [M1]
= 200 + 625 − 312.5
= 512.5 [A1]
∴ Maximum savings = $512.50

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WAEC 2023 Mathematics Question 8 Solution (Simultaneous Equation) - Step by Step




Question (WAEC 2023 Q7):

One-third of the sum of two numbers is 12, twice their difference is 12. Find the numbers.

Why students fail this:

WAEC marking scheme gives B1 for forming equations, M1 for adding, A1 for final answer. If you write only answer, you get 0.


Step 1: Notice that...

We have two unknown numbers. Let them be x and y.

First statement: one-third of sum is 12.

(1/3)(x + y) = 12
Multiply both sides by 3: x + y = 36 ... (i)

Second statement: twice their difference is 12.

2(x - y) = 12<br>
Divide by 2: x - y = 6 ... (ii)

Step 2: It follows that...

We now have two simple equations:
x + y = 36
x - y = 6

Add (i) and (ii): (x+y) + (x-y) = 36 + 6
2x = 42
x = 21

Step 3: Hence, find y
Substitute x = 21 into (i):

21 + y = 36
y = 36 - 21 = 15

Final Answer: x = 21, y = 15



Check

21+15=36,
one-third is 12 correct.

21-15=6, twice is 12 correct.



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Looking for a trusted procurement company in Nigeria? Welcome to **IWÁJÚ Procurement Services**—your reliable partner for sourcing and supplying quality products for schools, businesses, organizations, construction companies, and engineering projects.

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Why Selling on WhatsApp Feels Hard — And How Smart Sellers Are Fixing It




If you’ve ever tried selling products through WhatsApp status or Instagram, you already know one thing:



It looks easy from the outside — but the daily work can be exhausting.



At Iwajudrop, we’ve been talking to many small online sellers recently — students, WhatsApp vendors, fashion resellers, beauty vendors, boutique owners, gadget sellers, and even stay-at-home entrepreneurs.

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Most people are selling through WhatsApp + Instagram, but the process becomes stressful very quickly.



Here’s what many sellers deal with every day:


1. Sending product pictures repeatedly

A customer asks:

> “Do you have sneakers?”

You send pictures.

Another customer asks the same thing.

You send the same pictures again.

And again.

And again.

Instead of selling efficiently, many vendors spend hours repeating themselves in chats.

2. Answering the same questions every day

“How much?”

“Available?”

“Do you have size 42?”

“Can you deliver to Abuja?”

Same questions. Same replies. Every single day.

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3. Losing track of customer orders

One customer ordered in WhatsApp.

Another sent payment on Instagram.

Someone else asked for delivery details in DMs.

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4. No proper product catalogue

Many WhatsApp sellers don’t have a clean place to show products.

Everything is scattered:

* Old status posts
* Gallery photos
* WhatsApp chats
* Saved messages

So when customers ask:

> “What else do you sell?”

You start manually searching and sending products again.


5. Looking less professional

Let’s be honest.

Customers trust sellers who look organized.

If every conversation feels confusing or scattered, buyers may hesitate to pay — especially online.

People want confidence before sending money.


6. No single link to share

Most sellers still do everything manually.

Instead of simply saying:

> “See everything here”



They have to keep sending screenshots, pictures, videos, and prices one by one.

That takes time — and time affects sales.


The Real Problem? Most Sellers Don’t Need a Big Website

Here’s something interesting we noticed.

A lot of small sellers don’t actually want a complicated online store.

Many people hear about big e-commerce platforms and think:

> “That sounds expensive.”
> “Too technical.”
> “I just want something simple.”

What most WhatsApp sellers actually want is this:

✅ A clean catalogue of products
✅ One link to share with customers
✅ Easy setup
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In short:

They want a **simple system that helps them sell smarter — not harder.

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Jbamk:
Good day Nairalanders,

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Good day Nairalanders,

If you run a small or medium business and:

Customers complain about late replies

Leads stop responding after first contact

You can’t be online 24/7

WhatsApp chats are overwhelming

You’re losing sales.

I help SMEs set up AI-powered WhatsApp agents that:
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If you run or manage a school (private or public) and you’re tired of:

Overpriced supplies

Unreliable vendors

Delayed deliveries

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At IWÁJÚDROP, we’ve created something truly unique in the industry: a comprehensive sourcing and fulfillment operation that leverages partnerships with major wholesalers, supported by a dedicated team.

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Buying, purchasing, and procurement are often used interchangeably, but they're not the same thing.

- Buying is a simple transaction: you need something, you pay for it, and you get it. It's reactive, immediate, and doesn't involve much strategy or long-term thinking.
- Purchasing is more process-driven: it involves placing orders, negotiating prices, and ensuring goods and services are delivered correctly. Purchasing teams focus on cost control and accuracy, but it's still an operational role.
- Procurement is strategic: it's about building supplier relationships, managing risks, ensuring quality, and aligning purchases with company goals. Procurement involves market research, vendor management, compliance, and sustainability initiatives.

Treating procurement as a strategic function can lead to better cost savings, stronger supplier partnerships, and improved business resilience. Getting it wrong can lead to inefficiencies, missed opportunities, and financial losses.

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