Answer:
<u>The number of pens = 120 and the number of pencils = 200</u>
Step-by-step explanation:
Let the number of pens x, and the number of pencils is y
the cost of one pen $1, and the cost of one pencil $0.5
The cost of the whole purchase was $220
1 * x + 0.5 * y = 220
x + 0.5 y = 220 ⇒ eq.(1)
there were 80 more pencils than pens
y - x = 80 ⇒ eq.(2)
from eq.(2) x = y - 80
By substitution with x from the last equation at eq.(1)
∴ (y - 80) + 0.5 y = 220
1.5y = 220 + 80 = 300
y = 300/1.5 = 200
x = y - 80 = 200 - 80 = 120
<u>So, the number of pens = 120 and the number of pencils = 200</u>
Answer:
1/2
Step-by-step explanation:
6/12 = x/16
Answer:
Part c: Contained within the explanation
Part b: gcd(1200,560)=80
Part a: q=-6 r=1
Step-by-step explanation:
I will start with c and work my way up:
Part c:
Proof:
We want to shoe that bL=a+c for some integer L given:
bM=a for some integer M and bK=c for some integer K.
If a=bM and c=bK,
then a+c=bM+bK.
a+c=bM+bK
a+c=b(M+K) by factoring using distributive property
Now we have what we wanted to prove since integers are closed under addition. M+K is an integer since M and K are integers.
So L=M+K in bL=a+c.
We have shown b|(a+c) given b|a and b|c.
//
Part b:
We are going to use Euclidean's Algorithm.
Start with bigger number and see how much smaller number goes into it:
1200=2(560)+80
560=80(7)
This implies the remainder before the remainder is 0 is the greatest common factor of 1200 and 560. So the greatest common factor of 1200 and 560 is 80.
Part a:
Find q and r such that:
-65=q(11)+r
We want to find q and r such that they satisfy the division algorithm.
r is suppose to be a positive integer less than 11.
So q=-6 gives:
-65=(-6)(11)+r
-65=-66+r
So r=1 since r=-65+66.
So q=-6 while r=1.
Answer:
Let's say someone is selling lemonade at a lemonade stand. The more cups of lemonade this person sells, the more money they get. If 1 cup= $1, then he would get $2 for 2 cups.
Step-by-step explanation:
The price of the lemonade cup and the lemonade cup are a constant of proportionality. They are proportional to each other. The more lemonade you sell, the more money you get.
The graph would be a straight diagonal line. The y would be the money, and the x would be the amount of lemonade sold. Since they are the same and proportional, they would go in a straight line.
Answer:
A = 95238 (only)
Step-by-step explanation:
The question is equivalent to asking what n-digit number consisting only of the digit n will be divisible by n+1. Of the numbers 1, 22, 333, 4444, ... 999999999, the only one is 666666, which is divisible by 7.
The 5-digit integer A is 666666/7 = 95,238. There is only one instance of A.
