a and b together have \$ 1210. if \frac{4}{15} of as amount is equal to \frac{2}{5} of bs amount, how much amount does b have?

a) \$ 460
b) \$ 484
c) \$ 550
d) \$ 664

Question

a and b together have \$ 1210. if \frac{4}{15} of as amount is equal to \frac{2}{5} of bs amount, how much amount does b have?

a) \$ 460
b) \$ 484
c) \$ 550
d) \$ 664

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Proportional Reasoning", "Ratio Word Problems" ], "new_concepts": [], "current_concepts": [ "Proportional Reasoning", "Ratio Word Problems", "System of Linear Equations" ] } ## Set up the system of equations $$ \begin{aligned} A + B &= 1210 \ \frac{4}{15}A &= \frac{2}{5}B \end{aligned} $$ ## Express A in terms of B $$ \begin{aligned} A &= \frac{2}{5} \times \frac{15}{4} B \ A &= \frac{3}{2} B \end{aligned} $$ ## Solve for B $$ \begin{aligned} \frac{3}{2}B + B &= 1210 \ \frac{5}{2}B &= 1210 \ B &= 1210 \times \frac{2}{5} \ B &= 484 \end{aligned} $$

(A) \$ 460

(B) \$ 484

(C) \$ 550

(D) \$ 664

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Ratio Word Problems" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the system of equations

Express A in terms of B

Solve for B

Answer: