The snack stand at an ice-skating rink sells warm drinks to cold skaters. Skaters can choose from hot chocolate, apple cider, or coffee. Last weekend, skaters bought 126 cups of hot chocolate, apple cider, or coffee in all. They bought twice as many cups of hot chocolate as cups of apple cider. They bought 3 times as many cups of coffee as cups of apple cider. How many cups of hot chocolate did skaters buy last weekend?

The correct answer is 42

Step-by-step explanation:

You need to find how many cups of hot chocolate skaters bought last weekend. Start with the information in the problem.

Skaters bought 126 cups of hot chocolate, apple cider, or coffee in all.

They bought twice as many cups of hot chocolate as cups of apple cider.

They bought 3 times as many cups of coffee as cups of apple cider.

You can use a diagram to model the problem. Skaters bought the fewest number of cups of apple cider, so start with apple cider.

Skaters bought twice as many cups of hot chocolate as cups of apple cider. So, draw 1 box to represent the number of cups of apple cider and 2 boxes to represent the number of cups of hot chocolate.

apple cider

hot chocolate

coffee

Skaters bought 3 times as many cups of coffee as cups of apple cider. There is 1 box for apple cider. So, draw 3 boxes to represent the number of cups of coffee.

apple cider = 1 box

hot chocolate = 2 box

coffee = 3 box

There are 6 boxes in the diagram in all. Skaters bought a total of 126 cups of hot chocolate, apple cider, or coffee. So, each box represents 126÷6 cups. Divide.

21

6

126

–12

06

–  6

0

Each box represents 21 cups. There are 2 boxes for hot chocolate. Multiply to find the number of cups of hot chocolate skaters bought.

21

×  2

42

Skaters bought 42 cups of hot chocolate last weekend.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

i believe the answer is 323 ft

step-by-step explanation: