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if A gives B $3, B will have twice as much as A. If B gives A $5, A will have twice as much as...

Question:

If A gives B {eq}$3, {/eq} B will have twice as much as A. If B gives A {eq}$5, {/eq} A will have twice as much as B.How much does each have?

Algebraic equation word problems

An algebraic equation is formed when a relation between any variable is equated to a constant.

In the word problems of algebraic equation, the relationship is given in statement and we need to form an algebraic equation out of it. Assuming a base variable and determining other unknowns in its term also helps in simplifying the equation.

For example: It costs $400 for 4 adult tickets and 3 children ticket. It can be expressed as 4x +3y = 400 as an algebraic equation where x and y are variables representing the cost of one adult and children ticket each and 400 is the equivalent constant of the relation shown in the equation.

Answer and Explanation:

Let the amount of money with A and B be {eq}A and B {/eq} respectively.

According to the problem: A gives B $3, B will have twice as much as A

$$2*(A-3) = B+3 $$

$$2A-6 = B+3 $$

$$2A-B=9 $$

According to the problem: If B gives A $5, will have twice as much as B.

$$A+5 = 2(B-5) $$

$$A+5 = 2B-10 $$

$$2B -A=15 $$

Solving equations simultaneously:

$$(2B -A=15) + 2(2A-B=9) $$

$$3A = 33 $$

$$A = 11 $$

Using the value of A in the equation {eq}2B -A=15 {/eq}

$$2B -A=15 $$

$$2B -11=15 $$

$$2B =26 $$

$$B =13 $$

The amount of money with A and B is {eq}$11\ and\ $13 {/eq} respectively.


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