Adelivery truck is transporting boxes of two sizes: large and small. the large box weighs 60 pounds each, and the small box weighs 30 pounds each. there are 125 boxes in all. if the truck is carrying a total of 5700 pounds in boxes, how many of each type of box is it carrying

60 small boxes and 65 large boxes

Step-by-step explanation:

From the given information we can make two equations:

L + S = 125

60L + 30S = 5700

S represents the number of small boxes and L represents the number of large boxes.

To solve an equation we need there to be only one variable, so I solved for s in the first equation.

L + S = 125

S = 125 - L

Now I can plug this into the second equation

60L + 30S = 5700

60L + 30(125 - L) = 5700 (substitute S)

60L + 3750 - 30L = 5700

30L + 3750 = 5700 (combine like terms)

30L = 1950 (subtract 3750 from both sides)

L = 65 (divide both sides by 30)

Now that we know there are 65 larger boxes, plug in 65 for L to find S.

S = 125 - L

S = 125 - 65

S = 60

So there are 65 large boxes and 60 small boxes

There are 65 60-lb boxes and 60 30-lb boxes.

Step-by-step explanation:

Method:

Define two variables for the two unknowns. Set up a system of two equations in two variables. One equation deals with the numbers of boxes. The other equation deals with the weights. Solve the system of equations.

Define variables:

Let x = number of 60-lb boxes.

Let y = number of 30-lb boxes.

Equation dealing with numbers of boxes:

The total number of boxes is x + y. We are told the total number of boxes is 125, so the first equation is:

x + y = 125

Equation dealing with weights:

x number of 60-lb boxes weight 60x.

y number of 30-lb boxes weight 30y.

The total weight of all boxes is 60x + 30y. We are told the total weight is 5700 lb. The second equation is:

60x + 30y = 5700

System of two equations in two variables:

x + y = 125

60x + 30y = 5700

Solution of the system of equations by the substitution method:

Solve the first equation for x:

x + y = 125

Subtract y from both sides.

x = 125 - y

Substitute 125 - y for x in the second original equation.

60x + 30y = 5700

60(125 - y) + 30y = 5700

Distribute the 60.

7500 - 60y + 30y = 5700

Combine y-terms on left side.

7500 - 30y = 5700

Subtract 7500 from both sides.

-30y = -1800

Divide both sides by -30.

y = 60

There are 60 30-lb boxes.

Now substitute 60 for y in the first original equation and solve for x.

x + y = 125

x + 60 = 125

Subtract 60 from both sides.

x = 65

There are 65 60-lb boxes.

There are 65 60-lb boxes and 60 30-lb boxes.

Check:

The given information is there there are 125 boxes, and the total weight is 5700 lb.

The total number of boxes is 65 boxes + 60 boxes = 125 boxes. This checks with the given information.

The total weight is

65 * 60 lb + 60 * 30 lb = 3900 lb + 1800 lb = 5700 lb

This checks with the given information.

Our solution is correct.

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.