Set this up by translating the words into math concepts: “ratio of a number and 3 is equivalent to” translates to: x/3 = “difference of the number and 12” translates to: X – 12 So the equation is: x/3 = x - 12

You want to build a cement walk around a 24 ft x 49 ft garden If we let x = the width of the cement walk, then the outside dimensions of the walk will be (24 + 2x) and (49 + 2x) The garden itself will not be covered with cement, so the equation for the area of the walk...

Let A, B, and C = the three different teams. Then: A + B + C = 110 and we know that B = A - 10 C = B - 5 so substituting into the first equation, we have A + (A - 10) + (A - 10) - 5 = 110 combine like terms and solve: 3A...

Let R = number of radios Let P = the price she paid for each radio R*P = 1400 so P = 1400/R and (R-7)*(P+10) = 1400 substitute for P (R - 7)*(1400/R + 10) = 1400 and multiply 1400 -(7)(1400)/R + 10R - 70 = 1400 multiply...

You can use the midpoint formula, knowing the midpoint between two points (x1,y1) and (x2,y2) has the coordinates    [(x1 + x2)/2, (y1 + y2)/2]   Substituting what we are given, we get:   (2 + x2)/2 = 5   and   (5 + y2)/2 = 1   so,   2...

First, see that 80 liters of a 20% kool aid solution has 16 liters of kool aid, since 80x20% = 16   Now, we're going to add an amount of 59% kool aid to produce a total concentration of 30% kool aid.   So you can set it up as a proportion.  Let x = number of liters...

To solve this equation, manipulate the numbers so that the base numbers are the same. Since 4 = 2^2 we can rewrite this as: 2^3x = (2^2)^(x+2) Expanding the exponent gives: 2^3x = 2^(2x+4) Now that both bases are the same, we see that 3x = 2x+4 Solving...