Question

Two bowls and one cup weigh 800 grams. One bowl and two cups weigh 700 grams. Find the weight of the bowl and the cup

HELP

Answer 1

\large \boxed{\textbf{Bowl = 300 g; cup = 200 g}}

Explanation:

Let b = the mass of a bowl

and c = the mass of a cup

We have two conditions:

`\begin{array}{lrcl}(1) &2b + c & = & 800\\(2) & b + 2c & = & 700\\\end{array}`

Calculations:

`\begin{array}{lrcll}(3) & 4b + 2c &= & 1600&\text{ Multiplied (1) by 2}\\& 3b & = & 900&\text{Subtracted (2) from (3)}\\(4) & b & = & \mathbf{300}&\text{Divided each side by 3}\\ & 600 + c & = & 800&\text{Substituted (4) into (2}\\ & c & = & \mathbf{200}\\\end{array}\\\text{The mass of a bowl is $\large \boxed{\textbf{300 g}}$ and that of a cup is $\large \boxed{\textbf{200 g}}$}`

Check:

`\begin{array}{rlcrl}2(300) + 200& =800 & & 300 + 2(200) & = 700\\600 + 200 & = 800& & 300 + 400 & = 700\\800 & = 800& & 700 & = 700\\\end{array}`

OK.