Question

peter bought 16 more packets of sugar than salt. The mass of the packet of sugar is 422 g more than the mass of the packets of salt. A packet of sugar has a mass of 23 g and a packet of salt has a mass of 17g. How many packets of sugar did Peter buy?

Answer 1

Answer:

$\boxed{\sf Number \ of \ packets \ of \ sugar \ Peter \ bought = 25}$

Given:

Packets of sugar = 16 + Packets of salt

Mass of packets of sugar = 422 g + Mass of Packets of salt

Mass of one packet of sugar = 23 g

Mass of one packet of salt = 17 g

To Find:

Number of packets of sugar Peter bought.

Step-by-step explanation:

Let the number of packets of salt Peter bought be 'x'

$\therefore \\ \sf Packets \: of \: sugar = 16 + x$

$\sf Mass \ of \ Packets \ of \ sugar = Packets \\ \sf of \: sugar \times Mass \: of \: one \: packet \: of \: sugar \\ \\ \sf = (16 + x) \times 23 \\ \\ \sf Mass \ of \ Packets \ of \ salt = Packets \\ \sf of \: salt \times Mass \: of \: one \: packet \: of \: salt \\ \\ \sf = x \times 17 \\ \\ \sf = 17x$

$\therefore \\ \sf \implies Mass \: of \: packets \: of \: sugar = 422 + \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: Mass \: of \: Packets \: of \: salt \\ \\ \sf \implies (16 + x) \times 23 = 422 + 17x \\ \\ \sf \implies (16 \times 23) + (23 \times x) = 422 + 17x \\ \\ \sf \implies 368 + 23x = 422 + 17x \\ \\ \sf \implies 368 + 23x - 17x = 422 \\ \\ \sf \implies 368 + 6x = 422 \\ \\ \sf \implies 6x = 422 - 368 \\ \\ \sf \implies 6x = 54 \\ \\ \sf \implies x = \frac{54}{6} \\ \\ \sf \implies x = 9$

So,

Packets of salt = 9 Packets

Packets of sugar = 16 + Packets of salt

= 16 + 9

= 25 Packets