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%?

查看解析

登录即可查看完整答案

类似问题

Jonathan invested $6,220 in an account that pays 11 percent simple interest. How much money will he have at the end of 40 years?

A payday loan company charges 3.6 percent interest for a four-week period. What would be the annual interest rate from that company? Note: Assume an even 52 weeks per year. Enter your answer as a percent rounded to 1 decimal place. BlackTom题目解析

What is the total amount after 2 years if $3,030 is invested at a 6% annual simple interest rate? Please write the answer in two decimal places.

What is the total amount after 9 years if $10,301 is invested at a 8% annual simple interest rate? Please write the answer in two decimal places.

If you invest $6,866 at an annual simple interest rate of 14% for 8 years, how much interest will you earn? Please write the answer in two decimal places.

Henry bought an antique watch for $6,000 and sold it 9-months later for $6,360. What simple interest rate did he earn on this sale?

What is the formula for calculating simple interest?

Stella deposits $4,500 in a savings account at a bank that offers interest of 4.7% on such accounts. What is the value of the money in her savings account in one year's time?

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单