Question

ations of multi-step equations
complete the worksheet on lined notebook paper
define a variable and write an equation. then solve the equation
you must show inverse operations on both sides of the equation.
you must maintain the equation on all steps. each step is written below the previous step!
no ambiguous fractions.
money amounts must be written correctly (see the note in the lesson folder).
show all work! no work = no credit
1.
one number is nine more than another number. if the sum of the numbers is 65, find
both numbers.
2.
the sum of two numbers is 146. the larger number is 16 less than five times the
smaller number. find both numbers.
3.
eva and liam are reading a novel in their english class. liam has read 17 less pages
than eva has. if they have read 265 pages combined, how many pages has liam read?
4.
roger has two golden retrievers, sadie and buddy. buddy weights 14 pounds more
than sadie. if their total weight is 136 pounds, how much does sadie weigh?
5.
beth and carly are selling candy bars to raise money for new cheerleading uniforms.
beth has sold one less than twice the number of candy bars that carly has sold. if they
have sold 188 candy bars in all, how many has beth sold?
6.
mark flew from boston to baltimore, then baltimore to orlando. the number of people
on his first flight was five more than four times the number of people on his second
flight. if there were 365 people altogether on the two flights, how many were on the
flight from baltimore to orlando?
7.
morgan is making two cookie recipes. recipe a calls for one - third less than twice the
number of cups of sugar that recipe b calls for. if she needs four and one - sixths cups
of sugar in all, how many cups will she need for recipe a?
8.
on the album “1989” by taylor swift, blank space is 12 seconds longer than shake it
off. if the combined time of the two songs is 7 minutes and 30 seconds, how long is
shake it off? give the answer in minutes and seconds.
9.
the sum of two consecutive integers is 129. find both integers.
0.
the garden view hotel is 17 feet less than twice the height of the plaza hotel. if their
combined height is 361 feet, how tall is the garden view hotel?

Explanation:

Let's solve problem 1: "One number is nine more than another number. If the sum of the numbers is 65, find both numbers."

Step1: Define variables

Let the smaller number be $x$. Then the larger number is $x + 9$ (since it's nine more than the smaller one).

Step2: Set up the equation

The sum of the two numbers is 65, so we write the equation: $x + (x + 9) = 65$.

Step3: Simplify and solve for $x$

Combine like terms: $2x + 9 = 65$.
Subtract 9 from both sides: $2x = 65 - 9 = 56$.
Divide both sides by 2: $x = \frac{56}{2} = 28$.

Step4: Find the larger number

The larger number is $x + 9 = 28 + 9 = 37$.

Answer:

The two numbers are 28 and 37.