Final answer:
To set up and solve the equation for the word problem, we define the unknown number as y and express the difference between the number and 3 l as (y - 3 l). The equation is then 53 times (y - 3 l) = y - 76. After distributing and simplifying, we isolate y and arrive at the solution as y = (159 l - 76)/52.
Step-by-step explanation:
To set up the equation for this word problem, we need to break down the information given. Let's define the unknown number as y. The difference between a number and 3 l can be expressed as (y - 3 l). Now we can write the equation as 53 times (y - 3 l) is equal to the number plus -76, or 53(y - 3 l) = y - 76.
To solve this equation, we first distribute 53 to the terms inside the parentheses: 53y - 159 l = y - 76. Next, we can combine like terms by subtracting y from both sides: 53y - y - 159 l = -76. Simplifying further, we have 52y - 159 l = -76. To isolate y, we need to move the -159 l to the other side by adding it to both sides: 52y = 159 l - 76. Finally, we can solve for y by dividing both sides of the equation by 52: y = (159 l - 76)/52.
Learn more about Solving equations involving unknown numbers