You can also do it this way. The numbers are x, x+1 and x+2 x + x+1 + x+2 = 225 3x+3 = 225 3x = 222 x = 74 x+1 = 75 x+2 = 76

A full circle is 360°. What fraction of that is 140°? f = 140/360 = 7/18 You know how to calculate the area and circumference of a circle. Multiply each of those answers by 7/18. (Remember, C = pi*d = 2*pi*r)

a) e^0.053t is the population multiplier per year. For 1 year, that's e^0.053 = 1.0544. The growth rate is 5.44% per year.   b) For the population to double,  e^0.053t = 2 ln(e^0.053t) = ln(2) 0.053t = ln(2) = 0.693 t = 13.078 t ≈ 13 years

The longest dimension inside the box consists of a diagonal across the base and the height of the box. Diagonal: d2 = 2(282) d = √1568 d = 39.6 The bone will lie flat on the bottom of the box. Answer: Yes

The way to type these in line is to use parentheses: 6/(y+1) + y/(y-2) = 6/(y+1) • y/(y-2) The common denominator for the addition is: (y-1)(y+2) 6(y-2)/(y-2)(y+1) + y(y+1)/(y-2)(y+1) = 6y/(y-2)(y+1) These denominators are all the...

The first question asks for a "unit rate". It is miles per hour.  "Per" means divided by. Divide 8.64 by 2.4 8.64 / 2.4 = 3.6 mi/hr   The second question asks for the distance covered in 24 minutes, but our unit rate is in miles per hour, not miles...

"1/4 as many as 8 ..." is the same as "1/4 of 8" (1/4)*8   "... plus 2" add 2 to it.   (1/4)*8 + 2

Let A, B and C be the weights of the coffees. We have three equations.  The first two are straightforward. (1)  A+B+C = 50 (2)  C = 2A Substitute 2A for C in (1) (1)  A+B+2A = 3A+B = 50 (4)  B = 50-3A   (We'll use this for...

She gave 1/4 to her aunt.  She then had 3/4 left. She gave 1/2 of that to her grandfather.  1/2 * 3/4 = 3/8 Total she gave away was: 1/4 + 3/8 = 5/8 She then had 1 - 5/8 left for herself: 1 - 5/8 = 3/8 = 15 3/8 * P = 15   (P is the total picked.) P...

B = the speed of the boat in still water. S = the speed of the stream   Relative to the bank, the speed upstream is B-S. The speed downstream is B+S.   Use the equation for distance. Rate * Time = Distance Upstream (B-S)6 = 258 (B+S)6 = 330   Simplify...

Subtract the birth weight from the 6 month weight. 15 lb   9 oz  -6 lb 11 oz The problem is that you can't subtract 11 from 9. No problem! "Borrow" a pound (16 oz) from 15 and add it to the ounces. 14 lb 25 oz  -6 lb 11 oz   8 lb 14 oz

We need variable names for the original sum and the amount each person receives: S, A, B and C   Pick the statements apart to find pieces that you can write expressions/equations for. "Amanda receives \$1 plus ...: A = 1 + ... 1/3 of what is left. " What's...

A radian is a measure of the length of an arc.  The circumference of a circle is 2πr, so 2π radians is an arc that subtends 360 degrees. 1/2 pi radians is the arc created by a 90º angle.  That's 1/4 of a full circle.  The area of the full circle would thus be 4*98 = 392 cm^2...

Take is one small step at a time. Let their current ages be J, A and C.   The first statement is easy. "Jacob is 4 years older than Anthony": J = A+4   "Nine years ago..." Christopher was (C-9) and Anthony was (A-9) "Christopher...

Let S be the cost of one soda and P the cost of one popcorn. 4S + 3P = 27.25 5S + 6P = 47.00   Multiply the first equation by 2 and solve by elimination. 8S + 6P = 54.50 5S + 6P = 47.00   subtract   3S = 7.50 S= 2.50   Substitute...

The distance Zuza travels is 9 km east and 7 km north every 6 minutes. 6 minutes is 1/10 of an hour, so the distance he travels is 90t east and 70t north.   The airport is 3 km west and 5 km north from Krakow. You have to calculate the two distances, then add the distance to...

The graphs will be different when the calculated value is negative because the absolute value will be positive there. If ax^2+bx+c has real roots, it will cross the x-axis at those points.  Those points are where the graph crosses from positive to negative or vice versa. If...

Karen forgot to include the "Two times..." Two times the number of apples Mary has = 2M 2M - 12 = 50 2M = 62 M = 31   Of course this could also be interpreted as "Two times (the number of apples Mary has minus 12) is 50. That would be: 2(M-12)...

Let the number of 2-wheel and 3-wheel bikes be A and B. A + B = 27  (frames) The number of wheels required will be: 2A + 3B = 66 Substitution looks easier. A+B = 27 B = 27-A Substitute and solve for A 2A + 3B = 66 2A + 3(27-A) = 66 2A...

The first step is always to convert the English into equations to make it math problem. Read through the problem first to get the general idea of what's going on. With involved problems like this, look for things that you can write expressions or equations for, then figure out how to put...