Question 729873
1. A total of $12,000 is invested, part at 6% simple interest and part at 3%.
 If the annual return from the two investments is the same, how much is invested at each rate?
let x = amt invested at 6%
let y = amt invested at 3%
Two equations
x + y = 12000
and
.06x = .03y
divide both sides by .03, results
2x = y
replace y with 2x in the 1st equation
x + 2x = 12000
3x = 12000
x = 12000/3
x = 4000
I'll let you find y, check the solutions in the interest equation
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2. A car travels 225 kilometers in the same time that a truck travels 195 kilometers.
let x = car speed, let y = truck speed
write a time equation; time = dist/speed
{{{225/x}}} = {{{195/y}}}
Cross multiply
225y = 195x
divide both sides by 5, results:
45y = 39x
:
" If the speed of the car is 10 kilometers per hour faster than the speed of the truck,"
x - y = 10
x = y + 10
"find the speed of each vehicle."
replace x with (y+10) in the 1st simplified equation
45y = 39(y+10)
45y = 39y + 390
45y - 39y = 390
6y = 390
y = 390/6
y = 65 mph, the speed of the truck
I'll let you find the speed of the car, check your solutions in both equations