The cost of 2 cups and 3 plates is £18. The cost of 5 cups and 1 plate is £19. Let the cost of a cup be c.....

Question

and the cost of a plate bep. write tow simultaneous equations and solve them to find c and p.

Answer 1

2c + 3p = 18 (1)
5c + p = 19 (2)

(2) x 3

2c + 3p = 18 (3)
15c+ 3p = 57 (4)

(4) - (3)

13c = 39

c = 39/13
c = 3

So, a cup = £3

Put C= 3 into equation 2

15 + p = 19

p = 19-15

p = 4

So a plate = £4

Answer 2

First turn the sentences into equations:
2c+3p=18
5c+p=19

now solve for one of the variables in one of the equations
(solving for p in the second equation is easier)
5c+p=19
p=19-5c

now take the value for "p" and substitute/plug it into the other equation:
2c+3p=18
2c+3(19-5c)=18

now solve for c:
start by distributing the 3 into the parenthesis:
2c+57-15c=18

subtract 57 from both sides of the equation and combine like terms:
-13c=-39

divide both sides by -13
c=3

now you know that cups cost 3, now plug in that value into one of the original equations to find plates:
5c+p=19
5*3+p=19
15+p=19
p=4

plates cost 4 and cups cost 3

Answer 3

the cost of 1 cup is £ 3.

Answer 4

c=3
p=4
2c=6+{3x4}=18
5c=15+1p=4=19