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Graphing inequalities with calculator to find the maximum earnings of two part-time jobs

Q: Anna is a college student with two part-time jobs, one at a hardware store and the other at a fitness centre. She wants to work a minimum of 7 h/week at the hardware store, and 5h/week at the fitness centre . She does not want to work more than 15 h/ week. the . . . → Read More: Graphing inequalities with calculator to find the maximum earnings of two part-time jobs

A Farmer Wants to Maximize Area

Q: A farmer wants to put a fence around a vegetable garden. Only three sides must be fenced, since a rock wall will form the fourth side. If he uses 40m of fencing what is the maximum area possible?

A:  Okay, so we have two widths and one length.

The material used would . . . → Read More: A Farmer Wants to Maximize Area

Math 11: A Rectangle Word Problem using the Quadratic Formula

Formula for perimeter of a rectangle: P = 2w + 2l, where w=width and l=length

Formula for area of a rectangle: A = wl

30 = 2w+2l

40 =wl

In the area formula, isolate for l:

l = 40/w

Substitute this into the perimeter formula:

30 = 2w + 2(40/w) 30 = 2w + . . . → Read More: Math 11: A Rectangle Word Problem using the Quadratic Formula

Max/Min Rectangle Problem, Maximize the Area

Q: You have 128 feet of fencing to fence a rectangular area. Find the largest possible area to enclose this amount.

A: The perimeter of the space will be 128=2w+2L, where w=width and L=length

Isolate for L: L=64-w

The formula for the area of the rectangle is A=w*L. Substitute L=64-w into the area formula . . . → Read More: Max/Min Rectangle Problem, Maximize the Area

Max/Min Problem – Maximizing Revenue, Selling Calculators

Q: Calculators are sold to students for 20 dollars each. Three hundred students are willing to buy them at that price. For every 5 dollar increase in price, there are 30 fewer students willing to buy the calculator. What selling price will produce the maximum revenue and what will the maximum revenue be?

A: . . . → Read More: Max/Min Problem – Maximizing Revenue, Selling Calculators

Airplane with Tailwind and Headwind

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Q: An airplane flew 3 hours with a 40 mph head wind. The return trip with a tail wind of the same speed took 2 hours. Find the speed of the plane in still air.

A: When you have a headwind, you have to subtract the wind’s speed from the . . . → Read More: Airplane with Tailwind and Headwind

Rectangular pool with walkway, find areas

Q: A rectangular pool has a stone walkway around it. The total lenghth of the pool and walkway is 3 times the total width. The walk way is 2 feet all around. a) Write an expression for the area of the pool b) Find the area of the pool when the total width is . . . → Read More: Rectangular pool with walkway, find areas

Rectangular plot, find diagonals

Q: The area of a rectanglar plot is 12,000 square meters. If Kim walks along the diagonal from one corner to the opposiite corner instead of walking along the edges, she walks 60 meters less. What is the length of the diagonal? Thanks!

A: We need two Equations with two Variables. This is a . . . → Read More: Rectangular plot, find diagonals

Perimeter of a Rectangle, Two Unknowns

Q: The perimeter of a rectangle is 74 inches. If the width is doubled and the length is halved, the new rectangle will have a perimeter is 76 inches. What are the dimensions?

A: You have two unknowns, l=length and w=width, so you need two equations.

Recall that perimeter of a rectangle is P . . . → Read More: Perimeter of a Rectangle, Two Unknowns

Trail mix, mixture word problem

Q: The manager of a bulk foods establishment sells a trail mix for $10 per pound and premium cashews for $15 per pound. The manager wishes to make a 100-pound trail mix-cashew mixture that will sell for $14 per pound. How many pounds of each should be used?

A: Let x = pounds of . . . → Read More: Trail mix, mixture word problem