Hey all. Zaher wrote in with this practice problem while back, and I thought it’d make a good post, so here it is:
A room is 24 feet long, 18 feet wide, and 9 feet high. How many square yards of wallpaper are needed to paper the four walls of the room?
You got your basic area problem, right? How do I know it’s “area”? Well, area is the space on the surface of something. Like, how much carpet covers a floor, or how many tiles on a bathroom wall. Or paint on a room. If you’re covering a surface, you’re talkin’ area. Now, how to solve it?
You got a few bumps in the road. First, you got dimensions in feet, an’ you want an answer in yards. Whenever you got different measurements in a problem, I recommend always changin’ everything to the dimensions you want in yo’ answer first off. That means, changin’ all the feet to yards. Now, there’s three feet in a yard, and dat’s jus’ somethin’ you got to know. So, to change feet into yards, divide by 3.
24 feet = 8 yards
18 feet = 6 yards
9 feet = 3 yards
Hey, you gotta know you’re on the right track when all the numbers divide out evenly! Too bad real life don’t work dat way. ‘k. So’s, now it’s important to picture what the question’s about, specially with this kinda dimension question. You got a room, 8 yards by 6 yards, and 3 yards tall.
What’s the area of the 4 walls? That’s the real question… a wallpaper or carpet or tile (or anything that goes on a flat surface) question is an area question.
So… each wall got the same height, the height of the room…3 yards (9 feet):
wall 1: 3 yards × ?
wall 2: 3 yards × ?
wall 3: 3 yards × ?
wall 4: 3 yards × ?
So, what’s the width of the walls? well, 2 walls is 8 yards long (the two walls opposite of each other on the sides of the room that’re 24 feet) and 2 walls is 6 yards long (the two walls opposite of each other on the sides of the room that’re 18 feet).
wall 1: 3 yards × 8 yards
wall 2: 3 yards × 8 yards
wall 3: 3 yards × 6 yards
wall 4: 3 yards × 6 yards
To find the area, multiply:
wall 1: 3 yards × 8 yards = 24 square yards
wall 2: 3 yards × 8 yards = 24 square yards
wall 3: 3 yards × 6 yards = 18 square yards
wall 4: 3 yards × 6 yards = 18 square yards
And to find the total, add:
24 + 24 + 18 + 18 = 48 + 36 = 84 square yards
Answer’s 84!
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I am really having a hard time understanding translating word expressions into equations, and wondering if you can help?
Example:
1. the sum of 16 times a number and the number less another number times 3
2. a number less the sum of another number and 13
Yo Trish.
How these work is you gotta know what each word translates to in terms of math.
So, you got the word “sum” and that’s like the + sign. The word “times” is the × sign. If it says “a number” that’s a variable, or what’s usually written out as “x”. That means “the sum of 16 times a number” is:
16x +
Get it? Then it says “and the number less another number times 3.” When they talkin’ about “another number” then it’s another variable, which is “y.” The term “less” is subtraction. This is a tricky one. You gotta check to see if it’s “less” or “less than.” ‘Cause “3 less than 5″ would be:
5−3
But “3 less 5″ is like sayin’ “3 minus 5″ so it’d be:
3-5
Here, we just got “less” by itself, so we can see it as a “minus”:
x – 3y
Remember that ’cause it say “the sum of “16 times a number” AND “the number less another number times 3″ you should put that second part in parenthesis to group that side of the problem.
The whole equation would look like this:
16x + (x – 13y)
The second one would then be:
x – (y+13)
Make sense? This is a real good question. I had to really thinks about it. I’mma prolly put up a new blog post with some visuals about this problem, so keep an eye out for that. And good luck, girl.
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