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Question 1

Money Problems

Algebra is widely used to solve real-world financial situations such as pricing, budgeting, business transactions, and investments. Below are essential concepts that are commonly encountered in money-related algebra problems:

1. Cost Price (C or CP)

The original price or amount paid to purchase an item before any markup or discount.

2. Selling Price (S or SP)

The price at which an item is sold to a buyer. This may be greater than, less than, or equal to the cost price.

3. Markup

The amount added to the cost price to obtain the selling price. It reflects the seller's profit margin.

$$ \text{Markup} = \text{Selling Price} - \text{Cost Price} $$

4. Discount

A reduction in the original selling price, often given as a percentage.

$$ \text{Discount} = \text{Original Price} \times \left( \frac{\text{Discount Rate}}{100} \right) $$

5. Revenue

The total income generated from selling goods or services, without subtracting any costs.

$$ \text{Revenue} = \text{Selling Price} \times \text{Quantity Sold} $$

6. Profit

The financial gain made after subtracting total costs from total revenue.

$$ \text{Profit} = \text{Revenue} - \text{Total Cost} $$

7. Loss

Occurs when the selling price is less than the cost price.

$$ \text{Loss} = \text{Cost Price} - \text{Selling Price} $$

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Money Problems | Algebra – Problem 1: – Diagram

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Money Problems | Algebra – Problem 2: – Diagram

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Money Problems | Algebra – Problem 3: – Diagram

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Money Problems | Algebra – Problem 4: – Diagram

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Money Problems | Algebra – Problem 5: – Diagram

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Money Problems | Algebra – Problem 6: – Diagram

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Money Problems | Algebra – Problem 7: – Diagram

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Money Problems | Algebra – Problem 8: – Diagram

Answer

Let $x$ be Vigortab tablets and $y$ be Robust tablets. Minimize cost:
$C=0.50x+0.60y$
Subject to:
$3x+4y\ge24$, $20x+40y\ge200$, $40x+30y\ge120$.
Checking corner candidates, $x=0$, $y=6$ satisfies all requirements and gives the least cost:
$C=0.60(6)=3.6$
$\boxed{3.6}$

Answer

The marked total includes 8% sales tax, so:
$1.08C=34.56$
$C=\frac{34.56}{1.08}$
$\boxed{32}$

Answer

If $p$ includes 17.5% VAT, then:
$p=1.175(\text{pre-tax price})=\frac{47}{40}(\text{pre-tax price})$
VAT is 17.5% of the pre-tax price:
$v=0.175\left(\frac{40}{47}p\right)=\frac{7}{40}\cdot\frac{40}{47}p$
$\boxed{v(p)=\frac{7p}{47}}$

Answer

Marked selling price after 30% markup: $75(1.30)=97.50$.
After a 20% discount: $97.50(0.80)=78.00$.
Profit $=78.00-75.00=3.00$.
$\boxed{\text{P}3.00}$

Answer

Part 1.

Let $x$, $y$, and $z$ be the amounts invested at 12%, 10%, and 8%.
Since 1% more on each investment increases income by P2025, $0.01(x+y+z)=2025$, so $x+y+z=202500$.
Also $0.12x+0.10y+0.08z=21000$ and $0.12x=0.10y+0.08z$.
Solving gives $x=87500$, $y=65000$, and $z=50000$.
$\boxed{\text{P}87,500}$

Part 2.

Let $x$, $y$, and $z$ be the amounts at 12%, 10%, and 8%.
$x+y+z=202500$, $0.12x+0.10y+0.08z=21000$, and $0.12x=0.10y+0.08z$.
Solving the system gives $x=87500$, $y=65000$, and $z=50000$.
The 10% investment is $y=\text{P}65000$.
$\boxed{\text{P}65,000}$

Part 3.

Let $x$, $y$, and $z$ be the amounts at 12%, 10%, and 8%.
$x+y+z=202500$, $0.12x+0.10y+0.08z=21000$, and $0.12x=0.10y+0.08z$.
Solving gives $x=87500$, $y=65000$, and $z=50000$.
The 8% investment is $z=\text{P}50000$.
$\boxed{\text{P}50,000}$

Answer

Four coins have $2^4=16$ total outcomes.
The only outcome with no heads is all tails, so subtract 1.
Outcomes with at least one head $=16-1=15$.
$\boxed{15}$

Answer

Part 1.

Total coins: $20+30+24=74$. Drawing without replacement:
$P(\text{three 10-peso coins})=\frac{20}{74}\cdot\frac{19}{73}\cdot\frac{18}{72}=0.018$
$\boxed{0.018}$

Part 2.

Total coins: 74. Drawing without replacement:
$P(\text{three 5-peso coins})=\frac{30}{74}\cdot\frac{29}{73}\cdot\frac{28}{72}=0.063$
$\boxed{0.063}$

Part 3.

Total coins: 74. Drawing without replacement:
$P(\text{three 1-peso coins})=\frac{24}{74}\cdot\frac{23}{73}\cdot\frac{22}{72}=0.031$
$\boxed{0.031}$

Question 2

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Question 10

Question Bank: q245

MSTE - Algebra / Linear Programming / Engr. Janclyde Espinosa (Clidez)

Vigortab and Robust are two diet supplements. Each Vigortab tablet costs 50¢ and contains 3 units of calcium, 20 units of Vitamin C, and 40 units of iron. Each Robust tablet costs 60¢ and contains 4 units of calcium, 40 units of Vitamin C, and 30 units of iron. At least 24 units of calcium, 200 units of Vitamin C, and 120 units of iron are required for the daily needs of one patient. How many tablets of each supplement should be taken daily for a minimum cost? Find the daily minimum cost.

Answer:

3.6
3.8
4
3.2

Question 11

Question Bank: q264

MSTE - Algebra / Money and Investment Problems / Engr. Janclyde Espinosa (Clidez)

Kim is selling her anklet. Determine the cost of an anklet before tax if the total cost of an anklet, including 8% sales tax, is P34.56.

Answer:

32
36
30
33

Question 12

Question Bank: q273

MSTE - Algebra / Money and Investment Problems / Engr. Janclyde Espinosa (Clidez)

Value – added tax, VAT is a tax charged on goods and services in European countries. Many European countries offer refunds of some VAT to non – resident based businesses. VAT is included in a price that is quoted. That is, if an item is marked as costing 10, that price includes the VAT. Suppose an American company has operations in The Netherlands, where the VAT is 17.5%. Write a function for the VAT amount paid v(p) if p represents the price including the VAT.

Answer:

7p/47
40p/47
47p/40
7p/40

Question 13

Question Bank: t161

MSTE - Algebra / Algebra Fundamentals / Gemini mapped Chapter 1 to 3

A merchant purchased a pen at wholesale price of P75.00 and sells it at 30% markup. If a discount of 20% is given to a customer, how much profit can the merchant get?

P3.00
P7.50
P4.50
P5.00

Question 14

Question Bank: t169

MSTE - Algebra / Algebra Fundamentals / Gemini mapped Chapter 1 to 3

A man has three sums of money invested, one at 12%, one at 10%, and one at 8%. His total annual income from the three investments is P21,000.00. The first investment yields as much as the other two combined. If he should receive one percent more on each investment, his annual income would be increased by P2,025.00.

How much does he have invested at 12%?

P84,300
P88,800
P80,400
P87,500

How much does he have invested at 10%?

P63,200
P60,200
P64,200
P65,000

How much does he have invested at 8%?

P50,000
P45,000
P55,000
P60,000

Question 15

Question Bank: t238

MSTE - Algebra / Algebra Fundamentals / Gemini mapped Chapter 1 to 3

If four coins are tossed, how many possible ways are there for at least one coin showing head?

15
7
31
25

Question 16

Question Bank: t257

MSTE - Algebra / Algebra Fundamentals / Gemini mapped Chapter 1 to 3

A piggy bank has twenty 10-peso coins, thirty 5-peso coins, and twenty-four 1-peso coin. Three coins are drawn without replacement.

What is the probability that the three are 10-peso coins?

$0.048$
$0.063$
$0.031$
$0.018$

What is the probability that the three are 5-peso coins?

$0.031$
$0.018$
$0.048$
$0.063$

What is the probability that the three are 1-peso coins?

$0.018$
$0.063$
$0.031$
$0.048$

Money Problems

1. Cost Price (C or CP)

2. Selling Price (S or SP)

3. Markup

4. Discount

5. Revenue

6. Profit

7. Loss

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Exam Generator Problems

Question Bank: q245

Question Bank: q264

Question Bank: q273

Question Bank: t161

Question Bank: t169

Question Bank: t238

Question Bank: t257