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

 98 small cups and 57 large cups

Step-by-step explanation:

Use the information provided to create a system of equations:

                   Quantity     Cost      

Small cups:        x           $1.25x  

Large cups:       y           $2.50y          

         Total:      155         $265

Qty:    x   +  y   = 155 → -1.25(x + y = 155) → -1.25x - 1.25y = -193.75

Cost: 1.25x + 2.50y = 265              →           1.25x + 2.50y = 265.00

                                                                                  1.25y = 71.25

                                                                                         y = 57

Substitute "y" with "57" into either equation and solve for x:

x + y = 155

x + (57) = 155

x           = 98

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.