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

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

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%