Answer:
- <u>120 pens and 200 pencils.</u>
<u></u>
Explanation:
You can set a system of two equations.
<u>1. Variables</u>
<u />
- x: number of pens
- y: number of pencils
<u>2. Cost</u>
- <em>each pen costs</em> $1, then x pens costs: x
- <em>each pencil costs</em> $0.5, then y pencil costs: 0.5y
- Then, the total cost is: x + 0.5y
- The cost of the whole purchase was $ 220, then the first equation is:
x + 0.5y = 220 ↔ equation (1)
<u>3. </u><em><u>There were 80 more pencils than pens</u></em>
Then:
pencils = 80 + pens
↓ ↓
y = 80 + x ↔ equation (2)
<u>4. Solve the system</u>
i) Substitute the equation (2) into the equation (1):
ii) Solve
iii) Substitute x = 120 into the equation (2)
Solution: 120 pens and 200 pencils ← answer
Answer:
5
Step-by-step explanation:
for the first gear
revolutions/teeth
1 / 24
2 / 48
3 / 72
4 / 96
5 / 120
6 / 144
for the second gear
revolutions/teeth
1 / 40
2 / 80
3 / 120
4 / 160
<em>the two marks will meet after 120 teeth, 5 revolutions of the first gear and 3 revolutions of the second.</em>
the way to get that amount of teeth is
the Least Common Multiple equals the product of all factors, but those factors who are repeted for both numbers should be only once.
120 teeth are 5 revolutions for gear1 and 3 por gear2
Answer:
Let a be the width and b the length
a+3=b
a*b=54
a(a+3)=54
a^2+3a-54=0
a=6
The Answer is -16
I hope this helps
