# A one kilogram box of chocolates costs \$0.90 less than twice the cost of a box of a 500g box. Two one kilogram boxes and three 500g boxes cost \$34.60. Find  the cost of: a) one kilogram box b)...

A one kilogram box of chocolates costs \$0.90 less than twice the cost of a box of a 500g box. Two one kilogram boxes and three 500g boxes cost \$34.60. Find  the cost of:

a) one kilogram box

b) 500g box.

lemjay | High School Teacher | (Level 3) Senior Educator

Posted on

Let x be the cost of 1kg box of chocolate. And let y be the cost of 500g box of chocolate.

Then, express the given conditions is math form.

The first condition is that the x is 0.90 less than twice y. So, its math form is:

`x=2y-0.90`          (Let this be EQ1.)

And the second condition is that the cost of two x's and three y's is 34.60. So, its math form is:

`2x + 3y=34.60`      (Let this be EQ2.)

To solve for x and y, apply substitution method.

So, plug-in EQ1 to EQ2.

`2x + 3y = 34.60`

`2(2y-0.90)+3y=34.60`

`4y-1.80+3y=34.60`

`7y-1.80=34.60`

`7y-1.80+1.80=34.60+1.80`

`7y=36.40`

`(7y)/7=36.40/7`

`y=5.20`

Then, plug-in this value of y to EQ1.

`x=2y-0.90`

`x=2(5.2)-0.90`

`x=10.4-0.90`

`x=9.50`

Hence, the cost of 1kg box of chocolate is \$9.50 per box and the cost of 500g box of chocolate is \$5.20 per box.