Matthew invested $3,000 into two accounts. one account paid 3% interest and the other paid 8% interest. he earned 4% interest on the total investment. how much money did he put in each account?

Mathew invested $600 and $2400 in each account.

Solution:

From question, the total amount invested by Mathew is $3000. Let p = $3000.

Mathew has invested the total amount $3000 in two accounts. Let us consider the amount invested in first account as ‘P’

So, the amount invested in second account = 3000 – P

Step 1:

Given that Mathew has paid 3% interest in first account .Let us calculate the simple interest earned in first account for one year,

Where  

p = amount invested in first account

n = number of years  

r = rate of interest

hence, by using above equation we get as,  

----- eqn 1

Step 2:

Mathew has paid 8% interest in second account. Let us calculate the simple interest earned in second account,

Step 3:

Mathew has earned 4% interest on total investment of $3000. Let us calculate the total simple interest (I)

Step 4:

Total simple interest = simple interest on first account + simple interest on second account.

Hence we get,

By substituting eqn 1 , 2, 3 in eqn 4

12000=3P + 24000 - 8P

5P = 12000

P = 2400

Thus, the value of the variable ‘P’ is 2400  

Hence, the amount invested in first account = p = 2400

The amount invested in second account = 3000 – p = 3000 – 2400 = 600  

Hence, Mathew invested $600 and $2400 in each account.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

what graph

step-by-step explanation: