Question

Nico is saving money for his college education. He invests some money at 7%, and $1200 less than that amount at 3%. The investments produced a total of $174 interest in 1 yr. How much did he invest at each rate?
He invested $____at 7% and _____ at 3%.

Answer 1

Answer:

Nico invest $\ 2,100$ at 7% and $x=\ 900$ at 3%

Step-by-step explanation:

we know that

The simple interest formula is equal to

$I=P(rt)$

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

At 7%

$t=1\ years\\ P=\ x\\r=0.07$

substitute in the formula above

$I1=x(0.07*1)$

$I1=0.07x$

At 3%

$t=1\ years\\ P=\ (x-1,200)\\r=0.03$

substitute in the formula above

$I2=(x-1,200)(0.03*1)$

$I2=0.03x-36$

The total interest is equal to

I=I1+I2

I=$174

substitute

$174=0.07x+0.03x-36$

$0.10x=174+36$

$0.10x=210$

$x=\ 2,100$

$x-1,200=2,100-1,200=\ 900$

therefore

Nico invest $\ 2,100$ at 7% and $x=\ 900$ at 3%