I REALLY NEED HELP ON THIS QUESTION IM BEGGING YOU

Question

Ashley had a summer lemonade stand where she sold small cups of lemonade for $1.25 and large cups for $2.50. If Ashley sold a total of 155 cups of lemonade for $265, how many cups of each did she sell

And is HAS to be shown in elimination method or substitution method PLEASE

Answer 1

First, let's ask ourselves what do we want to know? We want to know how many cups of small and large lemonades were sold. Let's let S = # of small cups, and L the # of large cups.

It says she sold a total of 155 cups; that means S + L = 155. So this is one equation.

Next it says she made a total of $265. The small cups sold for $1.25 each, so she made $1.25S amount of money on these. It also says she sold large cups for $2.50 each, so she made $2.50L on these.

So, if we add up the money she made from each size, we can say 1.25S + 2.50L = 265.

Now we have two equations with 2 unknowns, and we can solve by either elimination or substitution. Let's solve it by substitution.

As S + L =155, L = 155 - S. Put this expression for L into the second equation.

1.25S + 2.50(155-S) = 265. Now solve this for S.

You should get S = 98 small cups. So, from the equation S + L = 155, solve for L which gives

L = 57 large cups. You can prove this by substituting these numbers in the second equation.

The same principles apply to other problems of this type.

Answer 2

Hi Syri,

This is a basic system of equations problem, so we should have two equations each with two variables. We can start by identifying the variables. The problem asks us to find the number of each size of cup sold, which we can define as the number of small cups (s) and the number of large cups (L). Now we need to create two equations. Our key is that we know the total number of cups sold and the total amount of money earned, each of which can be used to build an equation.

The total number of cups is a good place to start. We know 155 cups were sold in total, and that should be the same as the number of small cups sold plus the number of large cups sold: s + L = 155

The money equation is the trickier one. The total money earned, $265, should be equal to the amount of money earned from selling small cups plus the amount of money earned from selling large cups. If we multiplied the cost of a small cup ($1.25) by the number of small cups sold (s), we would find the money earned just from selling small cups. We can do the same thing with large cups. This gives us the following equation: 1.25s + 2.50L = 265

Finally, we need to solve for each variable. As you mentioned in your question, we can use either substitution or elimination. I will demonstrate using substitution. The idea here is that we can rearrange one equation to solve for one of the variables, then plug that into the other equation. It will be easiest to start with the first equation. We can solve for either variable, so I choose to solve for s.

s + L = 155

-L -L [Subtract L from both sides]

L = 155 - s

We don't know the actual number that L represents, but we know it is equal to 155 minus the number of small cups. We can take the other equation and replace L with 155 - s. That will leave us with an equation that has s as the only variable, meaning we can solve for s.

1.25s + 2.50L = 265

1.25s + 2.50(155 - s) = 265 [Substitution]

1.25s + 2.50*155 - 2.50s = 265 [Distribute 2.50]

1.25s + 387.5 - 2.50s = 265 [Multiply 2.5*155]

-1.25s + 387.5 = 265 [Combine like terms 1.25s and -2.50s]

-1.25s = -122.5 [Subtract 387.5 from both sides]

s = 98 [Divide both sides by -1.25]

We know our number of small cups sold: 98! Now we can return to either of the equations we made, plug in 98 for s, and solve for L. This will be easiest with the first equation.

s + L = 155

98 + L = 155

L = 57 [Subtract 98 from both sides]

So, 98 small cups were sold and 57 large cups were sold.

If we want to be extra thorough, we can plug both of those numbers into the second equation we made just to double-check that everything is correct:

1.25s + 2.50L = 265

1.25*98 + 2.50*57 = 265

122.5 + 142.5 = 265

265 = 265

Correct!

Answer 3