Mrs. Cheng invested $30,000 split into two accounts; one that earns 5% interest and the other earns 8% interest. The total interest on the investment was $2100. How much did she invest at a rate of 8%?

Question

BlackTom AI · Accepted Answer

We start by clarifying what we’re solving for: how much of the $30,000 is invested at 8%. Let x be the amount at 8%. Then the rest, $30,000 − x, is invested at 5%.

Compute the total interest earned from both portions: 0.08 × x from the 8% account and 0.05 × (30,000 − x) from the 5% account. The sum of these interests must equal $2,100, so:

0.08x + 0.05(30,000 − x) = 2,100.

Distribute the 0.05 across the parentheses: 0.08x + (0.05 × 30,000) − 0.05x = 2,100.

Since 0.05 × 30,000 = 1,500, the equation becomes:

0.08x + 1,500 − 0.05x = 2,100.

Combine like terms for x: (0.08 − 0.05)x = 0.03x, so 0.03x + 1,500 = 2,100.

Subtract 1,500 from both sides to isolate the term with x: 0.03x = 600.

Solve for x by dividing both sides by 0.03: x = 600 ÷ 0.03 = 20,000.

Thus, the amount invested at 8% is 20,000. If someone proposed 15,000, check by plugging back: interest from 8% would be 0.08×15,000 = 1,200 and from 5% on the remaining 15,000 would be 0.05×15,000 = 750; total would be 1,950, which does not reach 2,100, indicating the 15,000 figure cannot satisfy the given total.

In short, the equation method directly tests the balance between the two rates and confirms which portion aligns with the $2,100 total; the 8% portion must be the larger277, amount to satisfy the overall interest.

Mrs. Cheng invested $30,000 split into two accounts; one that earns 5% interest and the other earns 8% interest. The total interest on the investment was $2100. How much did she invest at a rate of 8%?

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