Question

# Two rival dry cleaners both advertise their prices. Let x equal the number of items dry cleaned. Store A’s prices are represented by the equation 15x - 2. Store B’s prices are represented by the expression 3 (5x + 7). When do the two stores charge the same rate ? Explain.

Hint:

### When a given equation has only 1 value that can be substituted for the variable which will satisfy the given equation, the said equation has only 1 solution. i.e. after simplifying the equation, we will get a single value as the solution for x.

We will simplify the given equation and the number of values we get for the variable.

## The correct answer is: Since LHS ≠ RHS for the given condition, the given situation has no solution

### Step-by-step solution:-

From the given information, we get-

Price charged by Store A = 15x - 2 …..................................... (Equation i)

Price charged by Store B = 3 (5x + 7)

∴ Price charged by Store B = 15x + 21 ….................................. (Equation ii)

We need to find the value of x for which the prices charged by the 2 stores are the same.

∴ Equating Equations i & ii, we get-

15x - 2 = 15x + 21

∴ 15x - 15x = 21 + 2 .................................................................... (Taking all variables and constants on either sides of the equation)

∴ 0 ≠ 23

∴ LHS ≠ RHS

Both the rivals have strategized their respective prices in such a way that for no number of items dry cleaned, the prices rates would be same.

Final Answer:-

∴ Since LHS ≠ RHS for the given condition, the given situation has no solution.

Mathematical expressions are made up of at least two numbers or variables, one math operation, and a sentence. This mathematical operation allows you to multiply, divide, add, or subtract numbers.

¶**Types of Expression**

1. Arithmetic operators and numbers make up a mathematical numerical expression. There are no symbols for undefined variables, equality, or inequality.

2. Unknown variables, numerical values, and arithmetic operators make up an algebraic expression. There are no symbols for equality or inequality in it.

¶In contrast to equations, the equal (=) operator is used between two mathematical expressions. Expressions denote a combination of numbers, variables, and operation symbols. The "equal to" sign also has the same value on both sides.