Page 9 !
Let Statements
Use a variable and algebraic expressions to set up “Let Statements” for the unknown quantities in the
sentences below.
1. The number of hours Bill works at his day job is 5 more than twice as his night job.!
The quantity mentioned second is the number of hours at his night job.
Night Job = x
The first sentence says that the hours at his day job is 5 more than twice his night job (2x).!
Add 5 at the end to twice as his night job (2x).
Day Job = 2x + 5
2. David wants to use four times as much red paint as blue paint in his picture.
The quantity mentioned second is blue paint.
blue paint = x
The first sentence says that the red paint is four times as much as the blue paint. (x)
Multiply 4 times the amount of blue paint. (4x)
red paint = 4x
3. The length of a rectangle is 4 less than three times the width.!
The quantity mentioned second is the width.
width = x!
The first sentence says the length is 4 less than three times the width (x).!
Subtract 4 from at the end of three times the width (3x).
length = 3x – 4!
4. The number of drinks Mary sold was 6 less than three times the number of hot dogs.
The quantity mentioned second is hot dogs.
hot dogs = x
The first sentence says that drinks are 6 less than three times the number of hot dogs (x).
Subtract 6 from the end of three times the number of hot dogs (3x).
!
drinks = 3x – 6
Math 30 !
Chapter 9 page 9 and 10!
© 2016 Eitel
5. Angle A is 6 degrees more than two times the measure of Angle B.!
The quantity mentioned second is Angle B.
Angle B = x
The first sentence says that Angle A is 6 degrees more than two times the measure of Angle B (x).
Add 6 at the end to two times the measure of Angle B (2x).
Angle B = 2x + 6
6. The second angle of a triangle is 5 less than two times the first angle.
The quantity mentioned second is ∠1.
∠1 = x
The first sentence says that second angle of a triangle is 5 less than two times the first angle (x).
Subtract 5 at the end from to two times the measure of first angle (2x).
∠2 = 2x – 5
7. The number of miles David runs is 6 less than 3 times the number of miles he walks.
!
The quantity mentioned second is the number of miles he walks.
walks = x
The first sentence says that runs is 6 less than 3 times the number of miles he walks (x).
Subtract 6 at the end from 3 times the number of miles he walks (3x)
.
∠2 = 3x – 6
8. The number of CD’s Sam has is 20 less than five times the number of his DVD’s
!
The quantity mentioned second is the number of of his DVD’s
DVD’s = x
The number of CD’s is 20 less than five times the number of his DVD’s (x)
Subtract 20 at the end from five times the number of his DVD’s (5x)
CD’s = 5x – 20
Math 30 !
Chapter 9 page 9 and 10!
© 2016 Eitel
9. Given 3 angles in a triangle , the second angle is 2 more than the first angle. The third angle
is 12 more than the first angle.!
In the first sentence the quantity mentioned second is the first angle
∠1 = x
The first sentence says that the second angle is 2 more than the first angle (x).
Add 2 at the end to the first angle (x)
∠2 = x + 2
The SECOND SENTENCE says that the third angle, ∠ 3 , is 12 more than the first angle (x).!
Add 12 at the end tothe first angle (x)
∠ 3 = x + 12
10. The first side of a triangle is 5 less than the second side. The third side is 4 more than twice
the second side.
In the first sentence the quantity mentioned second is the second side
S2 =x
In the first sentence the first side is 5 less than the second side (x).
Subtract 5 at the end from the second side (x)
S1 = x + 2
The second sentence says that the third side is 4 more than twice the second side.
Add 4 at the end to twice the second side (2x)
S 3 = 2x + 4
Math 30 !
Chapter 9 page 9 and 10!
© 2016 Eitel
Page 10
11. The first angle of a triangle is 15 more than four times the second angle. The third angle is 20
less than the second angle. !
! !
In the first sentence the quantity mentioned second is the second angle. ∠ 2
∠2 = x
In the first sentence the first angle is 15 more than four times the second angle (4=x).
Add 15 at the end to four times the second angle (4x).
∠1 = 4x + 15
The second sentence says that the third angle is 20 less than the second angle (x).
Subtract 20 at the end from the second side (x)
∠ 3 = x – 20
!
12. The number of houses that Mary sold is 12 less than three times as many as Joe sold. The
number of houses that Ann sold was 20 more than Joe sold.
In the first sentence the quantity mentioned second is houses Joe sold.
Joe sold = x
In the first sentence Mary sold is 12 less than three times as many as Joe sold (x).
Subtract 20 at the end from three times as many as Joe sold (3x).
Mary Sold = 3x – 12
The second sentence says that Ann sold was 20 more than Joe sold (x).
Add 20 at the end to the number Joe sold (x).
Ann Sold = x + 20
Math 30 !
Chapter 9 page 9 and 10!
© 2016 Eitel
13. The number of miles Sam runs is five less than 3 times the miles that Jim runs. The number
of David runs is 23 more than the number Jim runs.!
In the first sentence the quantity mentioned second is the miles that Jim runs..
Jim runs = x
In the first sentence Sam runs is five less than 3 times the miles that Jim runs. (3=x)
Subtract 5 at the end from 3 times the miles that Jim runs. (3x)
Sam runs = 3x – 5
The second sentence says David runs 23 more than the number Jim run (x).
Add 23 at the end to the number the number Jim run (x).
David runs = x + 23
!
!
!
!
14. The number of cars Bill sold is three times as many as the number of trucks he sold. The
number of vans he sold was 15 less than the trucks he sold.
In the first sentence the quantity mentioned second is the number of trucks sold.
Truck sold = x
In the first sentence the number of cars sold is three times as many as the number of trucks sold.
Multiply 3 times the the number of trucks sold (x).
Cars sold = 3x
The second sentence says the number of vans sold was 15 less than the trucks sold (3x).
Subtract 15 at the end from the number of trucks sold (x).
Van sold = x – 15
!
Math 30 !
Chapter 9 page 9 and 10!
© 2016 Eitel
NOTE: Read these problems carefully. There last 4 problems use a different comparison to get the
third let statement.
15. The first side of a triangle is 2 less than the second side. The third side is 12 more than the
FIRST SIDE. !
!
In the first sentence the quantity mentioned second is the second side.
S2 =x
In the first sentence the first side of a triangle is 2 less than the second side (x)
Subtract 2 at the end from the second side (x)
S1 = x – 2
The second sentence says the third side is 12 more than the FIRST SIDE WHICH IS (x – 2).
Add 12 at the end to the FIRST SIDE WHICH IS (x – 2).
S 3 = x – 2 + 12
!
!
16. The number of cars sold is 8 more than the number of trucks sold. The number of vans sold
is 3 less than the number of CARS sold.!
In the first sentence the the quantity mentioned second is the number of trucks sold
Trucks = x
In the first sentence the cars sold is 8 more than the number of trucks (x).
Add 8 at the end to the number of trucks (x).
Cars = x + 8
The second sentence says theThe number of vans sold is 3 less than the number of CARS sold
WHICH IS (x + 8).
Subtract 3at the end from the the number of CARS sold WHICH IS (x + 8).
Van sold = x + 8 – 3
Math 30 !
Chapter 9 page 9 and 10!
© 2016 Eitel
17.
The first angle of a triangle is 6 degrees more than the second angle. The third angle is 20
degrees less than the FIRST ANGLE.
In the first sentence the the quantity mentioned second is the second angle.
∠2 = x
In the first sentence the first angle of a triangle is 6 degrees more than the second angle.(x).
Add 6 at the end to the second angle.(x).
∠1 = x + 6
The second sentence says third angle is 20 degrees less than ∠1, WHICH IS (x + 6).
Subtract 20 at the end from ∠1, WHICH IS (x + 6).
∠ 3= x + 6 – 20
!
18. Given 3 angles, ∠ A is twice as large as ∠ B. ∠ D is 4 degrees more than ∠ A .
In the first sentence the the quantity mentioned second is ∠ B
∠B = x
In the first sentence ∠ Ais twice as large as ∠ B (x).
Multiply ∠ B (x) by 2,
∠ A = 2x
The second sentence says ∠ D is 4 degrees more than ∠ A . WHICH IS (2x).
Add 6 at the end to ∠ A . WHICH IS (2x).
∠ D = 2x + 6
Math 30 !
Chapter 9 page 9 and 10!
© 2016 Eitel