Question 104022
Let's name the two investments A and B. 
Write down what you know. 
"second investment, which is twice as large as the first"
1.{{{B=2A}}}
Rates and annual income...
2.{{{0.07*A+0.10*B=4050}}}
Substitute equation 1 into 2. 
{{{0.07*A+0.10*B=4050}}}
{{{0.07*A+0.10*(2A)=4050}}}
{{{0.07*A+0.20*A=4050}}}
{{{0.27*A=4050}}}
{{{A=15000}}}
Substitute your result into equation 1. 
{{{B=2A}}}
{{{B=2(15000)}}}
{{{B=30000}}}
Check your answer 
7% annual interest from $15,000 equals 
{{{(0.07)(15000)= 1050}}}
10% annual interest from $30,000 equals
{{{(0.10)(30000) = 3000}}}
{{{1050+3000=4050}}}
{{{4050=4050}}}
Good answer.