Mia has a jar containing nickels and dimes worth \$4.80 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 43m
- 2. Linear Equations and Inequalities5h 35m
- 3. Solving Word Problems2h 46m
- 4. Graphs and Functions5h 12m
- The Rectangular Coordinate System44m
- Graph Linear Equations in Two Variables24m
- Graph Linear Equations Using Intercepts23m
- Slope of a Line44m
- Slope-Intercept Form38m
- Point Slope Form22m
- Linear Inequalities in Two Variables28m
- Introduction to Relations and Functions53m
- Function Notation15m
- Composition of Functions17m
- 5. Systems of Linear Equations1h 53m
- 6. Exponents, Polynomials, and Polynomial Functions3h 17m
- 7. Factoring2h 49m
- 8. Rational Expressions and Functions3h 44m
- Simplifying Rational Expressions42m
- Multiplying and Dividing Rational Expressions25m
- Adding and Subtracting Rational Expressions with Common Denominators19m
- Least Common Denominators32m
- Adding and Subtracting Rational Expressions with Different Denominators32m
- Rational Equations44m
- Direct & Inverse Variation27m
- 9. Roots, Radicals, and Complex Numbers2h 33m
- 10. Quadratic Equations and Functions3h 1m
- 11. Inverse, Exponential, & Logarithmic Functions1h 5m
- 12. Conic Sections & Systems of Nonlinear Equations58m
- 13. Sequences, Series, and the Binomial Theorem1h 51m
3. Solving Word Problems
Mixture Problem Solving
Multiple Choice
A candy maker has of a sugar syrup. She wants to dilute it with pure water to make a syrup. How many of water should she add?
A
B
C
150mL
D
250mL
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Verified step by step guidance1
Identify the known quantities: the initial volume of syrup is 300 mL with 45% sugar concentration, and the desired concentration after dilution is 30%. Let the volume of water to add be \( x \) mL.
Express the amount of sugar before dilution: since the syrup is 45% sugar, the sugar amount is \( 0.45 \times 300 \) mL.
After adding \( x \) mL of water, the total volume becomes \( 300 + x \) mL, but the amount of sugar remains the same because water contains no sugar.
Set up the equation for the final concentration: the sugar amount divided by the new total volume equals 30%, so \( \frac{0.45 \times 300}{300 + x} = 0.30 \).
Solve the equation for \( x \) by multiplying both sides by \( 300 + x \), then isolating \( x \) on one side to find the volume of water to add.
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