🧮 algebra

1. **State the problem:** An airplane travels 1400 km in the same time a car travels 560 km. The car's speed is 200 kph less than the airplane's speed. We need to find the speed of

1. **State the problem:** A man is three times as old as his daughter. In twelve years, he will be twice as old as his daughter. We need to find their present ages. 2. **Define var

1. **Problem Statement:** When divided by $x - 3$, the polynomials $x^3 - px^2 + x + 6$ and $2x^3 - x^2 - (p + 3)x - 6$ leave the same remainder. Find the value of $p$. 2. **Formul

1. **State the problem:** Philip takes 9 hours longer than Jane to paint a car alone. Together, they paint the car in 6 hours. We need to find how long Jane takes to paint the car

1. **State the problem:** Solve the equation $$2^{x+7} - 2^{x+6} = 1$$ for $x$. 2. **Recall the properties of exponents:**

1. **State the problem:** Find all numbers $x$ such that the difference of the number and 3 equals half of the quotient of thrice the number and the sum of the number and two.

1. **State the problem:** Find all numbers $x$ such that the difference of the number and 3 equals half of the quotient of thrice the number and the sum of the number and two.

1. **State the problem:** A heptagon has a perimeter of 77 feet. Four sides are equal in length, and the remaining three sides are half as long as those four. We need to find the l

1. Let's solve a simple algebra problem suitable for Year 6 learners: Find the value of $x$ in the equation $2x + 3 = 11$. 2. The formula we use here is to isolate $x$ by performin

1. **State the problem:** We know that 50% of the children in the sports club go swimming, and 50% of those who swim also dive. We are told that 5 children both swim and dive. We n

1. **Problem:** Find the distinct roots of the quadratic equation $x^2 - 5x + 6 = 0$. 2. **Formula:** For a quadratic equation $ax^2 + bx + c = 0$, the roots are given by the quadr

1. **Problem Statement:** Find the value of the constant $k$ in the first table where $x$ and $f(x)$ values are given as: $$\begin{array}{c|c}

1. **State the problem:** Calculate the total daily wages paid by the factory. 2. **Write the expression:** Total wages = (Number of workers at 150 per day) \times 150 + (Number of

1. **State the problem:** We need to find the height of the NASA Space Shuttle's external tank. The height is calculated by adding 4 to the width and then multiplying by 8. The sum

1. Let's start by clarifying the problem you want to solve. Since you mentioned "that question" without specifying, I'll assume you want a general example of solving an algebraic e

1. **State the problem:** Solve the system of linear equations: $$0.08x + 0.15y = -0.76$$

1. **State the problem:** We need to find the height of the NASA Space Shuttle's external tank. The height is calculated by adding 4 to the width and then multiplying by 8. The sum

1. **State the problem:** We have two phone plans with different cost structures. We want to find the number of minutes where the total cost of Plan A equals the total cost of Plan

1. **State the problem:** We have two phone plans with different cost structures. Plan A costs $21 plus $0.13 per minute, and Plan B costs $0.17 per minute with no initial fee. We

1. The problem asks to write the expression $-x^{1/3} + \frac{9}{7} \cdot 2$ as one fraction with positive exponents. 2. First, simplify the constant multiplication: $\frac{9}{7} \

1. **State the problem:** A science class has 45 students total. The number of males is 13 more than the number of females. We need to find how many males and females are in the cl