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Word Problem Practice
WORD PROBLEM #3 - TAKING IT TO THE SOLAR SYSTEM
.
Together, Saturn, Jupiter, and Uranus have a total of 150 natural satellites (moons).
Jupiter has 3 more satellites than Saturn, and Uranus has 33 fewer satellites than
Saturn. How many satellites does each planet have?
If you let the number of satellites for Saturn be represented by the variable x, then
Jupiter must be represented as:
1.
and Uranus must be represented as:
Now write an equation in which the moons of Saturn, Jupiter, and Uranus add together
to total 150.
2.
3.
Use the space below to solve for x in the equation above, then fill in the following blanks.

Respuesta :

GinnyAnswer
Certainly! Let's solve the given word problem step by step.

Step 1: Define the Variables
Let x represent the number of satellites Saturn has.

Step 2: Express the Number of Satellites for the Other Planets
According to the problem:
- Jupiter has 3 more satellites than Saturn, so Jupiter has x + 3 satellites.
- Uranus has 33 fewer satellites than Saturn, so Uranus has x - 33 satellites.

Step 3: Write the Equation
The total number of satellites for all three planets is 150. So we write the equation that represents this total:
Saturn's satellites + Jupiter's satellites + Uranus's satellites = 150
Translating this into our variables, we get:
x (Saturn) + (x + 3) (Jupiter) + (x - 33) (Uranus) = 150

Step 4: Solve for x
Combine all the x terms and constants on one side of the equation:
x + (x + 3) + (x - 33) = 150

Combine like terms (the x terms and the constants):
3x + 3 - 33 = 150

Continue combining constants:
3x - 30 = 150

Step 5: Isolate x
Now to solve for x, add 30 to both sides of the equation:
3x - 30 + 30 = 150 + 30
3x = 180

Now divide both sides by 3 to solve for x:
3x / 3 = 180 / 3
x = 60

Step 6: Answer the Question
Now that we know x, which represents the number of satellites of Saturn, we can find the number for Jupiter and Uranus:
- Jupiter has x + 3 satellites, so Jupiter has 60 + 3 = 63 satellites.
- Uranus has x - 33 satellites, so Uranus has 60 - 33 = 27 satellites.

So, the final answer is:
- Saturn has 60 satellites.
- Jupiter has 63 satellites.
- Uranus has 27 satellites.