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