#18 mrs. rothberg baked 500 muffins on saturday and 3 times as many muffins on sunday. if the sold 5 muffins for $4, how much would she earn by selling her muffins on both days?
#19 jack had $80 more than eric. when jack spent $30, he found that the amount of money he had left was twice as much as what eric had. how much did the boys have altogether in the beginning?

1) She earn $1600 by selling her 2000 muffins on both days.

2) The amount of money boys have altogether in the beginning is $180.

Step-by-step explanation:

1) Given : Mrs. Rothberg baked 500 muffins on Saturday and 3 times as many muffins on Sunday. If the sold 5 muffins for $4.

To find : How much would she earn by selling her muffins on both days?

Solution :

On Saturday she manufacture = 500

On Sunday she manufacture =

Total manufacture on Saturday and Sunday is

She sold 5 muffins for $4.

She sold 1 muffin for .

She sold 2000 muffin for .

She sold 2000 muffin for $1600.

Therefore, she earn $1600 by selling her 2000 muffins on both days.

2) Given : Jack had $80 more than Eric. When Jack spent $30, he found that the amount of money he had left was twice as much as what Eric had.

To find : How much did the boys have altogether in the beginning?

Solution :

Let amount of money Jack has 'x'.

The amount of money Eric has 'y'.

According to question,

Jack had $80 more than Eric.

  .....(1)

When Jack spent $30, he found that the amount of money he had left was twice as much as what Eric had.

   .....(2)

Substitute the value of x in (2),

Substitute in equation (1),

The amount of money the boys have altogether in the beginning is

Therefore, the amount of money boys have altogether in the beginning is $180.

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west