Question

Sara spends $x on pens which cost $2.50 each.
She also spends $(x - 14.50) on pencils which cost $0.50 each.
The total of the number of pens and the number of pencils is 19.
Write down and solve an equation in x.​

Answer 1

If she spent $x on pens at $2.50 each, then she bought x/2.50 pens.
And similarly she bought (x - 14.50) / 0.50 pencils.

So x/2.50 + (x - 14.50) / 0.50 = 19

Rather than cross multiply, which only works for two equal fractions, multiply both sides by the least common denominator which is 2.50. That cancels both denominators, and you get

x + 5(x - 14.50) = 47.50

x + 5x - 72.50 = 47.50

6x = 47.50 + 72.50 = 120

so x = 120 ÷ 6 = 20