Box of beans and rice

Question

A cardboard box which weighs 0.6 pounds when empty is filled with 15 bags of beans and a 4 lb bag of rice The total weight of the box and the contents inside it is 25.6 pounds .One way to represent the situation is with the equation 0.6 + 15B + 4 = 25.6

In this situation, what does the solution to the equivalent represent 0.6 + 15B + 4 + 25.6

equation A 15b + 4=25.6

equation B 15b + 4 =25

equation C: 3(0.6 + 15b + 4)+76.8

equation D: 15b=25.6

equation E: 15b=21

Jada has a coin jar containing n nickles and d dimes worth a total of $3.65

The equation 0.05n + 0.1d+3.6s is one way to represent this situation.

Which equation is equivalent to the equation 0.05n + 0.1d =3.65

A. 5n+d=365

B. 0.5n+d=365

C. 5n+10d=365

D. 0.05d+0.1n= 365

Answer 1

Hi Joshua,

It looks like these problems are there to demonstrate steps to solving equations. An equivalent equation is one that equals the example equation - it just looks a little different from the original. That is because a step or two has been executed to change the numbers.

Remember, when solving equations, or looking for equivalent expressions, we want to do the same thing to both sides of the = sign. So, if I subtract .5 from the left side, I must subtract .5 from the right side.

Try looking at your initial equation, then at the answer choices. What would happen to your initial equation if you subtracted or added the same number to both sides? Is there anything in the answer choices that would represent one of these steps?

Sometimes it helps to eliminate the answer choices that you know can never equal the original. See what answer choices are left after you do that, and then play with different amounts you can add or subtract from both sides.

Hope that helps!

Answer 2

In the first problem, equations B and E are equivalent to the original problem. Equation B has .6 subtracted from both sides. Equation E also has 4 subtracted from both sides. All three equations have the same solution.

The solution represents the weight of one bag of beans in pounds.

In the second problem, C is the correct answer. It is 100 times the original problem. This removes the decimal fractions and makes all numbers integers. In effect, the problem is set up terms of pennies rather than dollars.

This reduces the possibility of error and is a good practice in general.