Mia has a jar containing nickels and dimes worth in total. If she has more dimes than nickels, how many of each coin does she have?
Table of contents
- 1. Review of Real Numbers2h 39m
- 2. Linear Equations and Inequalities3h 38m
- 3. Solving Word Problems2h 43m
- 4. Graphing Linear Equations in Two Variables3h 17m
- 5. Systems of Linear Equations1h 43m
- 6. Exponents and Polynomials1h 27m
- 7. Factoring2h 42m
- 8. Rational Expressions and Equations2h 18m
- 9. Inequalities and Absolute Value2h 52m
- 10. Relations and Functions1h 10m
- 11. Roots, Radicals, and Complex Numbers2h 33m
- 12. Quadratic Equations and Functions1h 23m
- 13. Inverse, Exponential, & Logarithmic Functions1h 5m
- 14. Conic Sections & Systems of Nonlinear Equations58m
- 15. Sequences, Series, and the Binomial Theorem1h 20m
3. Solving Word Problems
Mixture Problem Solving
Multiple Choice
A retirement fund invests some money in government bonds at annual simple interest, and \(5,000 more than that amount in corporate bonds at . If the total annual interest earned is \)1,450, how much was invested in each type of bond?
A
Government bonds = \$24,230.77; Corporate bonds = \$19,230.77
B
Government bonds = \$19,230.77; Corporate bonds = \$24,230.77
C
Government bonds = \$18,500.50; Corporate bonds = \$23,500.50
D
Government bonds = \$23,500.50; Corporate bonds = \$18,500.50
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Verified step by step guidance1
Let the amount invested in government bonds be represented by the variable \(x\).
Since the amount invested in corporate bonds is \$5,000\( more than the government bonds, express the corporate bonds investment as \)x + 5000$.
Write the expressions for the annual interest earned from each investment using simple interest formula: Interest = Principal \(\times\) Rate. For government bonds, the interest is \(0.025 \times x\), and for corporate bonds, it is \(0.04 \times (x + 5000)\).
Set up an equation for the total interest earned by adding the two interest amounts and equate it to the total annual interest of \$1,450$:
\(0.025 \times x + 0.04 \times (x + 5000) = 1450\)
Solve the equation for \(x\) to find the amount invested in government bonds, then add \$5,000$ to find the amount invested in corporate bonds.
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