Question

The price (p), in cents, of a sweet is directly proportional to the mass (m) of the

sweet.
When the sweet cost 55 cents, the mass is 220 g. Find
(a) the equation connecting p and m.
(b) the mass, in grams, of a sweet which cost 540 cents,
(c) the cost of a sweet in cents, with a mass of 115 g

Answer 1

The equation for constant proportionality is:

a = k • b where k is the constant

Since we are given the letter variables, replace a and b.

p = k • m

Part (a)

We know p = 55 cents when m = 220g, insert those values in equation:

55 = k • 220

55/220 = k

k = 1/4

Therefore, equation connecting p and m is:

p = 1/4 • m

Part (b)

We know p = 540 and we know k ( constant term )

540 = 1/4 • m

540 x 4 = m

m = 2160g

Part (c)

We know m = 115g, k is constant and therefore remains 1/4

p = 1/4 x 115g = 28.75 cents

~Hoodini, hope this helps.