🧮 algebra

1. **State the problem:** We want to find the equation for the cost $y$ of renting a backhoe for $x$ days, where $x$ is a positive integer and $x \leq 10$. The cost is $270 for the

1. **State the problem:** We need to find the y-coordinates of all points that satisfy the system of inequalities: $$y > 2x - 1$$

1. **State the problem:** Solve the inequality $$x^2 - 9x + 14 \leq 0$$. 2. **Identify the type of inequality:** This is a quadratic inequality. To solve it, we first find the root

1. **State the problem:** Ken earns $8 per hour for the first 10 hours and $10 per hour for the remaining hours. He saves 90% of his total earnings and wants to save at least 270.

1. The problem is to sketch the graph of the quadratic equation $$5x^2 + 19x - 4 = 0$$. 2. This is a quadratic function of the form $$y = ax^2 + bx + c$$ where $$a=5$$, $$b=19$$, a

1. **Problem 1:** An amount doubles in 5 years with compound interest. Find the time to become 8 times the original. 2. **Formula:** For compound interest, amount after $n$ years i

1. **State the problem:** We need to find the system of equations representing the original prices of a mirror ($m$) and a vase ($v$) given their combined original price and the co

1. **State the problem:** We are given the system of linear equations: $$-12x + 14y = 36$$

1. The problem is to find the equation of a line passing through two points or to analyze a given linear function. 2. The formula for the slope $m$ of a line passing through points

1. **State the problem:** We have two variables, $r$ and $b$, representing miles traveled at different speeds. The equations given are: $$5r + 10b = 200$$

1. Problem 56: A and B start a business. A invests 80000 for 9 months, B invests 120000 for 6 months. Find B's share of a 45000 profit. 2. Use the formula for profit sharing based

1. **State the problem:** Alice has $a$ chocolates and Bob has $b$ chocolates. Alice gives half of her chocolates to Bob. Then Bob gives half of all the chocolates he now has to Al

1. **State the problem:** We want to find how many liters of a 25% saline solution must be added to 3 liters of a 10% saline solution to get a 15% saline solution. 2. **Set variabl

1. **Problem 55:** Arvind, Bhavin, and Chandan invest in a business at different times and amounts. Total profit is 105000. Find Chandan's share. 2. **Formula:** Profit share is pr

1. **State the problem:** Calculate the value of the expression $$4 \frac{1}{12} + \frac{19}{5} - 0.41 \left(3.10\% + \frac{7}{4}\right)$$. 2. **Convert mixed numbers and percentag

1. **State the problem:** We have a line $k$ that intersects the y-axis at $(0, -6)$ and passes through $(2, 2)$. We need to find the value of $w$ for the point $(20, w)$ on the sa

1. **Problem statement:** (a) The normal price of a television set is 485 euros. It is reduced by 20% in a sale. Find the sale price.

1. The problem presents four linear equations labeled A, B, C, and D, each involving variables $x$ and $y$ with coefficients involving $R$ and constants $36$ or $-36$. 2. The goal

1. **Problem Statement:** We analyze the export data of Companies X, Y, and Z from 1993 to 1999 to answer several questions about their export changes.

1. **State the problem:** We are given a linear graph passing through points (0,10) and (2,6) and need to find the equation representing this linear relationship where $R$ is a pos

1. **Problem 1: Evaluate the expression** $7 \frac{1}{4} - \left[ \frac{5}{6} \div \left\{ \frac{1}{3} - \left( \frac{1}{2} \times \left( \frac{3}{4} - \frac{1}{4} \right) \right)