A mother wants to invest $$ \$ 7,000.00 $$ for her son's future education. She invests a portion of the money in a bank certificate of deposit (CD account) which earns $$ 4 \% $$ and the remainder in a savings bond that earns $$ 7 \% $$. If the total interest earned after one year is $$ \$ 420.00 $$, how much money was invested in the CD account? The total interest earned after one year is $$ \$ 420.00 $$. How much money was invested in the CD account? $$ \$ \square $$ (Round to the nearest cent, if necessary.)

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Let's denote the amount of money invested in the CD account as $$ x $$ dollars.

The remaining amount of money invested in the savings bond would be $$ \$7,000.00 - x $$ dollars.

The interest earned from the CD account after one year would be $$ 0.04x $$ dollars, and the interest earned from the savings bond after one year would be $$ 0.07(7000 - x) $$ dollars.

The total interest earned after one year is given as $$ \$420.00 $$, so we can set up the equation:

$$ 0.04x + 0.07(7000 - x) = 420 $$

Now, we can solve this equation to find the amount of money invested in the CD account.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$0.04x+0.07\left(7000-x\right)=420$$
- step1: Move the expression to the left side:
  $$0.04x+0.07\left(7000-x\right)-420=0$$
- step2: Calculate:
  $$-0.03x+70=0$$
- step3: Move the constant to the right side:
  $$-0.03x=0-70$$
- step4: Remove 0:
  $$-0.03x=-70$$
- step5: Change the signs:
  $$0.03x=70$$
- step6: Divide both sides:
  $$\frac{0.03x}{0.03}=\frac{70}{0.03}$$
- step7: Divide the numbers:
  $$x=\frac{7000}{3}$$
The amount of money invested in the CD account is $$ \$2,333.33 $$ (rounded to the nearest cent).
The amount invested in the CD account is $$ \$2,333.33 $$.

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