GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsMedium
A nutritionist is creating a diet plan that involves two types of protein bars. Bar A contains 15 grams of protein and Bar B contains 20 grams of protein. If a client wants to consume exactly 100 grams of protein by eating a total of 6 bars, how many of Bar A should they eat?
- A3 bars
- B4 bars
- C2 bars
- D5 bars
Show answer & explanationAnswer & explanation
Correct answer: B. 4 bars
Let 'a' be the number of Bar A and 'b' be the number of Bar B. We have two equations: a + b = 6 (total bars) and 15a + 20b = 100 (total protein). From the first equation, b = 6 - a. Substitute this into the second: 15a + 20(6 - a) = 100. Simplify: 15a + 120 - 20a = 100. Combine like terms: -5a + 120 = 100. Subtract 120: -5a = -20. Divide by -5: a = 4. So, 4 of Bar A should be eaten.
Why the other options are wrong
- A. This would result in 45g from A and 60g from B (3 bars), totaling 105g, not 100g.
- C. This would result in 30g from A and 80g from B (4 bars), totaling 110g, not 100g.
- D. This would result in 75g from A and 20g from B (1 bar), totaling 95g, not 100g.
Solving Systems of Linear Equations (Substitution)
A method to find the values of variables that satisfy two or more linear equations simultaneously by solving one equation for a variable and substituting that expression into the other equation.
- Isolate one variable in one of the equations.
- Substitute the expression for that variable into the other equation.
- Solve the resulting single-variable equation.
- Substitute the found value back into one of the original equations to find the other variable.
Memory trick: Substitution: Swap it out, then solve it!