Question

4D+5P=$25

3D+4P=$26

Find the Value of D and P

Answer 1

P = 29, D = - 30

Explanation:

Given the 2 equations

4D + 5P = 25 → (1)

3D + 4P = 26 → (2)

Multiplying (1) by 3 and (2) by - 4 and adding the result will eliminate D

12D + 15P = 75 → (3)

- 12D - 16P = - 104 → (4)

Add (3) and (4) term by term to eliminate D

0 - P = - 29

- P = - 29 ( multiply both sides by - 1 )

P = 29

Substitute P = 29 into either of the 2 equations and solve for D

Substituting into (1)

4D + 5(29) = 25

4D + 145 = 25 ( subtract 145 from both sides )

4D = - 120 ( divide both sides by 4 )

D = - 30

Answer 2

P= $29 and D = -$30

Explanation:

4D + 5P = $25

5P = $25 - 4D

P = ($25 - 4D)/5 equation(i)

Noe substitute the value of P

3D + 4P = $26

3D + 4($25 -4D)/5 = $26

3D*5 + ($100 -16D)/5 =$26*5

15D + $100 - 16D =$130

-D = $130 - $100

D = -$30

Again substitute the vale of D in equation(i)

P = ($25 + 4D)/5

=$25 + 4*$30/5

=$25 + $120/5

=-$145/5

=$29