Please help me with the following question

Question

I buy a packet of sugar and a packet of rice. The rice is 2 1/2 times as heavy as the sugar. Sugar cost $1.10 a kilogram and rice costs $1.25 a kilogram. I pay the shopkeeper with a $10 and get back a change of $1.55. Find the mass of the packet of rice.

Answer 1

Hi Kevin,

 

Let X = the mass of the sugar that was bought

 

Then 2.5X = the mass of rice that was bought . . . one packet of each was purchased.

 

You paid 10 - 1.55 = $8.45

 

So  1.10X + 1.25(2.5)X =  8.45

 

1.10X + 3.125X = 8.45

 

4.225X = 8.45

 

X = 2 = mass of sugar

 

Multiplying by 2.5 gives us 5 kg for the mass of rice.

 

Dan