Let the three numbers be x, y, and z.
If the sum of the three numbers is 3, then x+y+z=3
If subtracting the second number from the sum of the first and third numbers gives 9, then x+z-y=9
If subtracting the third number from the sum of the first and second numbers gives -5, then x+y-z=-5
This forms the system of equations:
[1] x+y+z=3
[2] x-y+z=9
[3] x+y-z=-5
First, to find y, let's take do [1]-[2]:
x+y+z=3
-x+y-z=-9
2y=-6
y=-3
Then, to find z, let's do [1]-[3]:
x+y+z=3
-x+-y+z=5
2z=8
z=4
Now that you have y and z, plug them into [1] to find x:
x+y+z=3
x-3+4=3
x=2
So the three numbers are 2,-3, and 4.
Answer: 2 days
Step-by-step explanation:
The monkeys eat 3 ²/₃ buckets of bananas each day. Convert this to an improper fraction:
= 3²/₃ = 11/3 buckets per day
The zookeeper bought 7¹/₃ which is:
= 22/3 buckets
To find out the number of days the bananas will last, divide the buckets bought by the buckets eaten per day:
= 22/3 ÷ 11/3
= 22/3 * 3/11
= 66/33
= 2 days
<em>If dividing fractions, multiply by the reciprocal of the second fraction. </em>
Answer:
4x² + 12 = 7x
4x² + 12 - 7x = 0
use the quadratic formula and get your answer!
Step-by-step explanation:
We begin with 1,000 fish in a lake.
Each year the population declines to 15%
Then they put back 500 fish in the lake.
The equation: (1000 * .85) +500
Answer:
The first mechanic charges $105 per hour, and the second mechanic charges $90 per hour.
Step-by-step explanation:
If x is the rate of the first mechanic, and y is the rate of the second mechanic, then:
10x + 5y = 1500
x + y = 195
Solve the system of equations using elimination or substitution. Using substitution:
10x + 5 (195 − x) = 1500
10x + 975 − 5x = 1500
5x = 525
x = 105
y = 195 − x
y = 90
The first mechanic charges $105 per hour, and the second mechanic charges $90 per hour.
