Section 2 – 3 HW:
Solving Equations with Proportions
Selected Worked Homework Problems
Solve each proportion for x. Show all steps. Reduce answers with fractions to decimal form.
1.
4 8
= !
5 x
12 6
= !
x 7
2.
Cross multiply and solve for x
Cross multiply and solve for x
4 • x = 5• 8
6 • x = 12 • 7
4 x = 40
divide both sideds by 4
!
6x = 84
divide both sideds by 6
x = 10
3.
x = 14
x 7
=
!
8 2
2 3
= !
9 x
6.
Cross multiply and solve for x
Cross multiply and solve for x
2• x = 7• 8
2 • x = 3• 9
2x = 56
divide both sideds by 2
2x = 27
divide both sideds by 2
x = 28
!
27
2
divide 2 into 27 to get a decimal
x=
x = 13.5
Math 100 !
Section 2–3 HW WKD !
© 2016 Eitel
8.
x 7
= !
10 4
5 12
=
8 x
10.
!
Cross multiply and solve for x
Cross multiply and solve for x
4 • x = 7 •10
5 • x = 12 • 8
4 x = 70
!
divide both sideds by 4
70 35
x=
=
4
2
divide 2 into 35 to get a decimal
x = 17.5
5x = 96
divide both sideds by 5
96
x=
5
divide 5 into 96 to get a decimal
x = 19.2
7
x
11.
= 3 !
15
5
12.
Cross multiply and solve for x
Cross multiply and solve for x
5 • x = 15 •
6
8
=
9
x
4
7
3
7
5 • x = 1/ 5/ 5 • 1
3/
5x = 35
divide both sideds by 5
6• x = 8•
!
9
6 • x = 8/ 2 • 1
4/
6x = 18
divide both sideds by 6
x=7
Math 100 !
9
4
x=3
Section 2–3 HW WKD !
© 2016 Eitel
13.
John notices that a 6 foot tall tree has a 3 foot shadow. He wonders how tall a nearby tree is
that has a 39 foot shadow.
Sentence 1.
The ratio of tree height to shadow is 6 feet tall to 3 foot shadow
6 feet tall
3 foot shadow
Sentence 2.
The ratio of tree height to shadow is unknown height to 39 foot shadow
unknown height in feet
39 foot shadow
6 feet tall
x height in feet
=
3 foot shadow 39 foot shadow
cross multiply and solve for x
3• x = 6 • 39
3x 6/ 2 • 39
=
3
3/ 1
x = 78 feet
Check:
6 feet tall
78 feet tall
=
3 foot shadow 39 foot shadow
2 feet tall
2 feet tall
=
1 foot shadow 1 foot shadow
Math 100 !
Section 2–3 HW WKD !
© 2016 Eitel
14. The scale on a map states that 2 inches on the map is equal to 30 miles in the real world. If the
distance on a map is 7 inches apart how many miles are the actual cities apart?
Sentence 1.
The ratio of map to real world is 2 inches on map to 30 miles in real world
2 inch map
30 miles in real world
Sentence 2.
The ratio of map to real world is 7 inches on map to unknown miles in real world
7 inch map
unkown miles in real world
2 inch map
7 inch map
=
30 miles in real world x miles in real world
cross multiply and solve for x
2 • x = 7 • 30
2x 7 • 3/ 0/ 15
=
2
2/ 1
x = 105 miles in real world
Check:
2 inch map
7 inch map
=
30 miles in real world 105 miles in real world
1 inch map
1 inch map
=
15 miles in real world 15 miles in real world
Math 100 !
Section 2–3 HW WKD !
© 2016 Eitel
3
inches on the map is equal to 6 miles in the real world. If the
4
actual distance between two cities is 48 miles, how many inches will they be apart on the map?
19. The scale on a map states that
Sentence 1.
3
The ratio of map to real world is inches on map to 6 miles in real world
4
3
inches on map
4
6 miles in real world
Sentence 2.
The ratio of map to real world is unknown inches on map to 48 miles in real world
unknown inches on map
48 miles in real world
3
inches on map
x inches on map
4
=
6 miles in real world 48 miles in real world
cross multiply and solve for x
6• x =
6• x =
3
• 48
4
3
• 4/ 8/ 12
1
4/
6x = 36
x = 6 inches on map
Math 100 !
Section 2–3 HW WKD !
© 2016 Eitel