Math Question that deals with weight and all that jazz?

Question

Tom has 3 blue blocks and 6 pink that weigh 14 pounds all together. Lucy has 3 pink blocks and the weigh the same as 2 blue blocks. How muck does a blue block weigh, and how much does a pink weigh?

Answer 1

If x is the weight of a blue block and y is the weight of a pink block, we can say

3x + 6y = 14
3y = 2x

to create a system of equations. Use the second equation to get an expression for x in terms of y. Substitute that expression for x into the first equation to solve for a numerical value for y, and then use that value in either equation to solve for x as well.

Answer 2

3 blue + 4 blue (= 6 pink) =14 lb => 1 blue = 2 lb
and 1 pink = 2/3 blue = 2*2/3 lb = 1 1/3 lb

Answer 3

Let's see if we can write equations for those conditions.
Let b be the weight of blue blocks, and p the weight of pink.

3b+6p = 14
3p = 2b

Good, those equations can be solved:
3b+6p = 14
6p = 4b
substitute eqn 2 into eqn 1:
3b + 4b = 14
7b = 14
b = 2

now plug that into eqn 1:
3*2+6p = 14
6p = 8
p = 8/6 = 4/3

Now check:
3*2+6*(4/3) =? 14
6+8 =? 14
14 =? 14 , this checks

3*(4/3) =? 2*2
4 =? 4 , this checks.

That's your answer.

Answer 4

Assume blue block weighs 'b' pounds each and pink block weighs 'p' pounds.
3b+6p=14
3p=2b
solving these two simultaneous equations:
b=2 pounds, p=4/3 pounds