Solve the system by substitution: 3x + 4y = 18 and y = 2x - 3. Provide exact values.

A rectangular playground's length is 3 times its width minus 5 feet (length = 3 × width – 5). The perimeter is 290 feet. Solve for the width, then calculate the length.

A taxi charges a flat fee of \$3 plus \$2.00 per mile. If you have a \$23 budget for the ride, how many whole miles can you afford?

Using the formula A = lw for rectangle area, find the area when l = 7.5 m and w = 4 m by following identify, substitute, and solve steps.

From the formula I = V/R for electric circuits, compute R when V = 12 V and I = 2.5 A.

The magnification formula for a camera lens is M = f / (f - d), where f is the focal length in mm and d is the object distance in mm. If f = 50 mm and d = 100 mm, compute M and specify its unit, or indicate if M is unitless.

Convert $12.5\%$ to both a fraction in simplest form and its decimal equivalent.

Solve for $x$ in the equation derived from the statement: "$15$ is $15\%$ of $x$."

Jake borrows $\$2,000$ at a simple interest rate of $4.5\%$ per year for $3$ years. How much interest will he owe at the end of the $3$-year period?

Which general form captures the mixture equation for two parts with quantities x and (T − x) and unit values a and b producing total value V?

A chemist needs to create 14 liters of a 50% acidic solution. They have two different acidic solutions available to use each with percentages of 40% and 70% respectively. If $x$ represents the number of liters for the 40% solution, how many liters of each solution should they mix together in order to achieve their desired acidic solution?

Three different sugar syrups (A, B, C) are to be combined, but only the total mass and overall concentration are specified. If the concentrations of A, B, and C are 5%, 10%, and 20% respectively, and the total mass is M, explain why you cannot uniquely determine all three masses from only the total mass and overall percentage, and give an expression showing one variable in terms of the other two.