Quiz #4 (2.6, 2.7) Name: _____Solution______
Math 102
Solve the following problems – make sure you work is very clear.
1. One side of a triangle is half the longest side. The third side is 10 meters less than the longest side.
The perimeter is 45 meters. Find all three sides.
Call the longest side x. Then the first side is
/ 2
x
and the third side is
10
x
−
. The perimeter is given
by the sum of all three sides, so we get the equation:
( 10) 45
2
10 45
2
2 5 2
55 55 22 .
5 2 5
x
x x
x
x x
x x m
+ − + =
⇒+ + − =
⇒=⇒= ⋅ =
Now we state the answer in terms of the actual lengths:
Long side: 22m.
Medium side: x-10 = 12m.
Small side: x/2 = 11m.
2. Money is invested into two accounts: one earns
10%
interest annually, and the other earns 4%
interest annually. There is twice as much money in the 4% account as there is in the 10% account.
The total interest earned in one year is $90. How much money is in each account?
Interest earned in a year:
Amount in 10% account: x 0.1x
Amount in 4% account: 2x 0.04(2x)
Total interest equation:
(
)
100 .1 .04( 2 ) 90 10 4(2 ) 9000 18 9000 $500
x x x x x x+ = ⇒+ = ⇒=⇒=
There is $500 in the 10% account and $1000 in the 4% account.