Elsie took all her cans and bottles from home to the recycling plant. The number of cans was one more then four times the number of bottles. She earned 12 cent for each bottle and 10 cent for each can, and ended up earning $2.18 in all. How many cans and bottles did she recycle ?

pendejos give us the answers

Let's start by assigning variables to the unknown quantities. Let's say the number of bottles is "b" and the number of cans is "c".

Given that the number of cans was one more than four times the number of bottles, we can write the equation:

c = 4b + 1

The total amount Elsie earned is $2.18. Since she earned 12 cents for each bottle, the total amount earned from bottles is 12b. Similarly, since she earned 10 cents for each can, the total amount earned from cans is 10c. So we can write another equation:

12b + 10c = 218

Now we have a system of two equations:

c = 4b + 1
12b + 10c = 218

To solve this system, we can substitute the first equation into the second equation:

12b + 10(4b + 1) = 218

12b + 40b + 10 = 218
52b + 10 = 218

52b = 218 - 10
52b = 208

b = 208 / 52
b = 4

Now we can substitute the value of "b" into the first equation to find "c":

c = 4(4) + 1
c = 16 + 1
c = 17

Therefore, Elsie recycled 4 bottles and 17 cans.

To solve this problem, we need to set up equations based on the given information and use algebra to find the values of the variables.

Let's say the number of bottles that Elsie recycled is "b" and the number of cans is "c".

According to the problem, the number of cans is one more than four times the number of bottles. So, we can write the first equation as:

c = 4b + 1 --- Equation 1

Now, Elsie earns 12 cents for each bottle and 10 cents for each can. The total amount she earned is $2.18. We can express this information mathematically as:

12b + 10c = 218 --- Equation 2 (in cents)

To make the equations more manageable, we can convert the total amount she earned to cents.

Now, we have a system of two equations (Equations 1 and 2) with two unknowns (b and c). We can solve this system by substitution or elimination.

Let's solve the system by substitution:

We can substitute the value of c from Equation 1 into Equation 2:

12b + 10(4b + 1) = 218
12b + 40b + 10 = 218
52b + 10 = 218
52b = 218 - 10
52b = 208
b = 208 / 52
b = 4

Now, we can substitute the value of b into Equation 1 to find the value of c:

c = 4(4) + 1
c = 16 + 1
c = 17

Therefore, Elsie recycled 4 bottles and 17 cans.

c = 4b+1

.12b + .10c = 2.18

Now just solve for b and c