We can see that Terri paints 1/3 of her living room in an hour.  Angela paints 1/4 of the living room in an hour. So, together they can paint 1/3 + 1/4 of the living room in an hour. 1/3 + 1/4 = 4/12 + 3/12 = 7/12. So, together they can paint 7/12 of the living room in an...

We are asked to investigate a8/a3=a5    We can expand these expressions to obtain    a.a.a.a.a.a.a.a/a.a.a   Since a/a =1, we can rewrite these expressions as   a/a . a/a . a/a . a.a.a.a.a   = 1.1.1.a.a.a.a.a   and...

The surface area of a rectangular prism (our box) is 2 * the ends + 2 * the sides + 2 * top (or bottom).   So using our dimensions it is   2 * (a*2a) + 2 * (a*1) + 2 * (2a*1)  = 4a^2 + 2a + 4a = 4a^2 + 6a.   Now we can say that...

If we create two variables, one for the length (L) and the other for the width (W), we can write two equations to model this situation:   The length is twice the width, so  L = 2W.   and the perimeter is equal to the area (with different units), so   2L +...

Since we are probably not going to give 2 trophies to the same float, we are able to say that any one of the 50 floats could win the 1st place prize, and any one of the 49 remaining floats could win 2nd place.  So to calculate the total number of possible outcomes we have to multiply those...

Using Heather's pay rate of \$6.55/hour and her 25 hours worked we multiply to find that she earned 25 * \$6.55 which is \$163.75 last week.   Her deductions are \$42.11, which we will subtract from her gross, giving \$163.75 - \$42.11 = \$121.64.   So she gets \$121.64 to spend...

If there were exactly equal numbers of beads in the box, there would be 125 blue and 125 yellow.   Since there are 60 fewer yellow than blue, there are 125 - (60/2) yellow, and 125 + (60/2) blue.   125 - (60/2) = 125 - 30 = 95, so there are 95 yellow beads in the box...

The total volume of your pool is 36 * 18 * 5 = 3240 cubic feet.  And there are 7.48 gallons in a cubic foot So, in gallons, the total volume of your pool is 3240 * 7.48 = 24,235.2 gallons. So, since we can get 4 gallons/minute, it will take 24,235.2/4 minutes to fill the pool =...

We have to look at the 300m/s at 42 degrees as a combination of two velocities, a vertical velocity and a horizontal velocity.   So, using trigonometry, the vertical velocity is 300m/s * sin 42 degrees and the horizontal velocity is 300m/s * cos 42 degrees.   So vertical...

If we begin by looking at the Granny Smith apples, we can say that   5 apples per pie and six apples per applesauce has to equal 194 apples   So 5p + 6s = 194.   We can then look at the Golden Delicious apples, and say that   3 apples per pie...

Assuming that they can each contribute to the job together at the same rate as if they were working alone,   Grady does 1/8 of the job each hour, and Cleo does 1/10 of the job each hour,   So together they do 1/8 + 1/10 of the job each hour = 9/40 of the job each hour...

I am going to assume that you mean an annual interest of 15%, payable for each day that the loan is outstanding.   The formula for the future value of a loan is <Loan amount> times <1+interest rate> ^<loan period>   where <loan amount> is the...

We can look at this either by specifying the number of small trucks, or the number of big trucks.  I am going to specify the number of high-capacity trucks, which I am going to label 'h'.   Now I am going to express the number of possible low-capacity trucks (l) in terms of the...

Looking at the equation, x+y=8, I can subtract either x or y from both sides to get the following two equations: x = 8 - y,     or    y = 8 - x. So I now have an expression which I can substitute for either x or y. Now, looking at the equation,...

Changing the subject of a formula on the mathisfun.com page refers to rearranging an equation to solve for a different variable.  This can only be done using valid algebraic operations, always remembering that both sides of the equation have to be changed in equivalent ways so that the equal...

When you have a system of equations, there are three main methods for solving it: Elimination, substitution, and graphing. The choice of which method to use is based on the equations. If you can easily multiply one of the equations by a factor you choose and then subtract the resulting...

The goal of this question is to use algebraic methods to solve the equation A = (B x C) / (B + D) for an expression involving A and D only.      A = (B x C) / (B + D)                                 ...

Actually, I think Victoria's answer is incorrect. Her method is correct, but her solution doesn't work: Given that the perimeter is twice the length plus twice the width, and the length is 30 inches longer than the width, we can indeed make an equation as follows: 2L + 2W = 208 and...

I am assuming that the container is a cylinder with a diameter of 8m and a height of 15m. The surface area would mean the top, the sides, and the bottom. The top and bottom would both be circles of diameter 8m, and the sides would be a rectangle of height 15m and width the circumference...

The problem posed is 5-3*54. Now, 54 is 5*5*5*5. What, however, is 5-3?0 Now, 53 is 5*5*5 and 52 is 5*5. Extending this, 51 is 5 and 50 is 5/5 which is 1 So 5-1 would be 1/5, 5-2 would be 1/(5*5), and 5-3 would be 1/(5*5*5). So, 5-3*54 is (5*5*5*5)/(5*5*5) = 5....