Real Life system of equations

Question

The Frosty Ice -Cream Shop sells sundaes for $2 and banana splits for $3. On a hot summer day , the shop sold 8 more sundaes than banana splits and made $156. How many sundaes and banana splits were sold

Answer 1

S: Sundaes

B: Banana splits

System of equations:

2S + 3B = 156

S = 8 + B

Replace S in the first equation:

2(8 + B) + 3B = 156

16 + 2B + 3B = 156

5B = 156 - 16

5B = 140

B = 140 / 5

B = 28

Replace B in the second equation:

S = 8 + B

S = 8 + 28

S = 36

They sold 28 Banana splits and 36 Sundaes.

Answer 2

So let's start off by declaring both of the unknown variables: the number of sundaes and the number of banana splits. Let us say that:

"b" is the number of banana splits sold

"s" is the number of sundaes sold.

Now that we have our variables, we need to start working on the equations. Our first equation will be:

3b + 2s = 156

This equation takes the unknown number of deserts sold, each respectively multiplied by the amount they sell for to equal the amount made. The second equation will look like this:

s - b = 8

This equation means that there are 8 more sundaes sold than banana splits. Now with both of our equations, we can go ahead and solve the problem.

3b +2s = 156

s - b = 8

Our first step is to take one of the equations and isolate one of the unknown values. The value you choose isn't important, just try and pick the easier one. in this instance, I'll be modifying the 2nd equation.

s - b = 8

+b +b

s = 8 + b

So now that we have "s" isolated, we can say that "s" is equal to "8 + b," and we can take this knowledge and substitute it into the 1st equation (substituting it into the same equation will result in zeroing it out).

3b + 2s = 156

3b + 2(8 + b) = 156

And from here, we go ahead and solve the problem as usual until "b" is isolated.

3b + 2(8 + b) = 156

3b + 16 + 2b = 156

5b + 16 = 156

5b = 140

b = 28

So now we have the total number of banana splits sold! To find "s," just plug in the value for "b" and solve as usual

s - (28) = 8

s = 36

And so our final answer is:

s = 36

b = 28

Answer 3

Hmm... reminds me of eeples and baneenees for some reason.

Let's use some short-hand symbols for some of these items:

s = # of sundaes sold

b = # of banana splits sold (notice how I don't just say "banana splits," because "b" only stands for the number sold, not their temperature or size or... etc.

1. Stuff written in "math" should be readable in English (or any language). *

We have TWO relationships described by our mysterious Client:

1.) the NUMBER relationship: << the shop sold 8 more sundaes than banana splits >>

2.) the COST relationship: << the shop sold 8 more sundaes than banana splits and made $156 >>

Using our short-hand,

1.) s = b + 8 or perhaps s = 8+b

Read it: "The number of sundaes sold IS eight more than the number of banana splits sold."

2.) $2s + $3b = $156

"The money made from selling sundaes and banana splits IS EQUAL to $156."

If we drop "units symbols" until we get back to the Client, we now have

1.) s = b + 8

2.) 2s + 3b = 156

This is a "2x2 system," a set of 2 equations containing 2 unknown values. This can be solved by "substitution" of (b+8) for s in the 2nd statement, or by "elimination" of one of the variables, or some other ways as well. If there is no solution, you will find that out also!

If you need any more to get to the solution just post a response here!

Regards,

:PC