2.3 Practice: Word Problems With Multiple Unknowns* For #1-5, define the variable, write an equation, and solve it. Write your answer in a complete sentence. 1. Mary’s sister is 7 years older than Mary. Their combined ages add up to 35. How old is Mary? 2. The sum of Ali and Mel’s age is 39. If Mel is 3 years younger than twice Ali’s age, how old are Ali and Mel? 3. The sum of two consecutive integers is 131. Find the integers. 4. The sum of three consecutive integers is 96. Find the integers. 5. The sum of the two numbers is 98. The larger number is one less than twice the smaller number. Find both numbers. For #6, the variables are defined for you. Write a word problem to match the equation. Solve and answer in a complete sentence. Defined Variables & Equation Word Problem Answer (in a complete sentence) 6. a = Lisa’s age now a + 3 = Bart’s age now Equation: a + 3 + a 19

1. let Mary be X years old

let Mary's sister be Y years old

Mary's sister is 7 years older than Mary

Y= 7 + X

their combined ages add up to 35

Y + X = 35

7 +X + X = 35

7 + 2X =35

2X = 35 - 7

2X = 28

X = 14

Y = 7 +X

Y = 7 + 14 = 21

Mary is 14 while Mary's sister is 21

2. Age of Mel is 25 years.

It is given that,the sum of Ali and Mel's age is 39. If Mel is 3 years younger than twice Ali's age.

Let 'x' be the Ali's age  and 'y' be the Mel's age

To find the value of x and y

sum of Ali and Mel's age is 39

x + y = 39(1)

Mel is 3 years younger than twice Ali's age

y = 2x - 3(2)

2x - y = 3(3)

(1) + (3)  

 x + y = 39

2x - y = 3

3x   = 42

x = 42/3 = 14

y = 2x - 3 = 14*2 - 3  = 25

Therefore the age of Ali = 14

Age of Mel = 25

3. x, x+1

x+x+1=131

2x+1=131

2x=131-1=130

x=130÷2 = 65

the integers are 65 and 66

4. Let the smallest number = n

Short 31 32 33

Let the second number = n + 1

Let the 3rd number = n + 2

Let the sum = s

s = 96

s = n + n + 1 + n + 2 Collect like terms.

s = 3n + 3

96 = 3n + 3  Subtract 3 from both sides

96 - 3 = 3n  Collect like terms on the left

93 = 3n  Divide by 3

93/3 = n

n = 31 

So the 3 consecutive numbers are

31 , 32, 33 

5. Let the larger number = y and the smaller number = x.

The largest number is 10 less than twice the smaller number.  Remember that less than means subtract the 10 from the other amount while twice means multiply by two.  Therefore,

y = 2x - 10

The sum of the two numbers is 38.  Remember sum means add the two numbers to get their result.  Therefore,

x + y = 38

Since y = 2x - 10, we rewrite the lower equation as:

x + (2x - 10) = 38

Solving:

3x - 10 = 38

3x = 48

x = 16

The lesser number is 16 and the greater number is 2(16) - 10 or 22.

6. the last one im a lil stuck on

so, converting firstly the mixed fractions to improper fractions and then "adding".