the length of a rectangle is (x-3) inches long, and the width 3 2/5 inches. If the area is 15 3/10 square inches, write and solve an equation to find the length of the rectan

To find the length of the rectangle, we can use the formula for the area of a rectangle:

Area = Length × Width

Given that the width is 3 2/5 inches, we need to convert it to a mixed number:

3 2/5 = (3 × 5 + 2)/5 = 17/5

Let's write the equation using the information given:

15 3/10 = (x - 3) × (17/5)

To solve the equation, we need to simplify the right-hand side by distributing the (17/5) to (x - 3):

Multiplying fractions: (17/5) × (x - 3) = (17(x) - 17(3))/(5)

Next, we combine like terms:

15 3/10 = (17x - 51)/5

To eliminate the fraction, we can multiply each term by 5:

(5) × (15 3/10) = (5) × ((17x - 51)/5)

On the left-hand side, we convert the mixed number to an improper fraction:

(5) × (15 + 3/10) = (5) × (150/10 + 3/10) = (5) × (153/10)

After simplifying, we have:

(153/10) = 17x - 51

To isolate x, we add 51 to both sides:

(153/10) + (51) = 17x - 51 + 51

Multiplying fractions: (153/10) + (51) = (153 + 510/10) = 663/10

663/10 = 17x

Finally, we divide both sides by 17 to solve for x:

(663/10) ÷ 17 = (663/10) ÷ (17/1)

Dividing fractions: (663/10) ÷ (17/1) = (663/10) × (1/17) = 663/170

Therefore, the length of the rectangle is:

x = 663/170 inches

I just did this below.

Thanks