Math  /  Algebra

QuestionCapucine played a game where she earned 179 points from building 11 museums and 4 libraries. She earns 4 more points per museum than per library.
How many points does Capucine earn for each thing she builds?

Studdy Solution

STEP 1

What is this asking? We're trying to figure out how many points Capucine earns for building one museum and one library. Watch out! Don't forget that museums earn 4 more points than libraries!
Keep an eye on those extra points.

STEP 2

1. Define the variables
2. Set up the equations
3. Solve the system of equations

STEP 3

Alright, let's start by **defining our variables**!
We'll call the points earned for each library L L and the points earned for each museum M M .
Remember, museums earn more points than libraries.

STEP 4

Now, let's **set up our first equation**.
Capucine built 11 museums and 4 libraries, earning a total of 179 points.
So, we can write:
11M+4L=17911M + 4L = 179This equation represents the total points from both museums and libraries.

STEP 5

Next, we know that each museum earns 4 more points than each library.
So, we can write our second equation as:
M=L+4M = L + 4This equation captures the relationship between the points for museums and libraries.

STEP 6

Let's **substitute the second equation** into the first one to eliminate M M and solve for L L .
Substitute M=L+4 M = L + 4 into 11M+4L=179 11M + 4L = 179 :
11(L+4)+4L=17911(L + 4) + 4L = 179

STEP 7

Now, let's **expand and simplify** the equation:
11L+44+4L=17911L + 44 + 4L = 179Combine like terms:
15L+44=17915L + 44 = 179

STEP 8

Next, we'll **solve for L L ** by isolating it on one side.
Subtract 44 from both sides:
15L=13515L = 135

STEP 9

Finally, **divide both sides by 15** to find L L :
L=9L = 9So, Capucine earns **9 points per library**!

STEP 10

Now, let's find M M using the equation M=L+4 M = L + 4 :
M=9+4=13M = 9 + 4 = 13Capucine earns **13 points per museum**!

STEP 11

Capucine earns **9 points** for each library and **13 points** for each museum.

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