A bank loaned out $17,500, part of it at the rate of 12% annual interest, and the rest at 10% annual interest. The total interest earned for both loans was $1,940.00. How much was loaned at each rate?

___was loaned at 12% and
___was loaned at 10%

$9500 was loaned at 12%

$8000 was loaned at 10%.

Step-by-step explanation:

Let x represent the amount which the bank loaned out at the rate of 12% annual interest.

Let y represent the amount which the bank loaned out at the rate of 10% annual interest..

The bank loaned out $17,500, part of it at the rate of 12% annual interest, and the rest at 10% annual interest. . This means that

x + y = 17500

The formula for determining simple interest is expressed as

I = PRT/100

Considering the amount loaned out the rate of 12% annual interest.

P = $x

T = 1 year

R = 12℅

I = (x × 12 × 1)/100 = 0.12x

Considering the amount loaned out the rate of 10% annual interest,

P = $y

T = 1 year

R = 10℅

I = (y × 10 × 1)/100 = 0.1y

The total interest earned for both loans was $1,940.00, it means that

0.12x + 0.1y = 1940 - - - - - - - - - -1

Substituting x = 17500 - y into equation 1, it becomes

0.12(17500 - y) + 0.1y = 1940

2100 - 0.12y + 0.1y = 1940

- 0.12y + 0.1y = 1940 - 2100

- 0.02y = - 160

y = - 160/ - 0.02

y = 8000

x = 17500 - y = 17500 - 8000

x = 9500

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

~