Alvin has $760 less invested in 7% than he has at 5%. If his annual income from these two investments is $51.20, how much does he have invested at each rate?

Answer:Alvin invested $110 at rate of 7% and invested $870 at rate of 5% Step-by-step explanation:we know that The simple interest formula is equal to [tex]I=P(rt)[/tex] where I is the 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 Letx------> the amount of money invested at rate of 5%At rate of 7%we have [tex]t=1\ years\\ P=(x-\$760)\\r=0.07[/tex] At rate of 5%we have [tex]t=1\ years\\ P=x\\r=0.05[/tex] substitute in the formula[tex]51.20=(x-760)(0.07*1)+(x)(0.05*1)[/tex] [tex]51.20=0.07x-53.2+0.05x[/tex] [tex]51.20+53.2=0.12x[/tex] [tex]x=104.4/0.12=\$870[/tex] thereforeAlvin invested ($870-$760)=$110 at rate of 7% Alvin invested $870 at rate of 5%