Step-by-step explanation:
these are almost the simplest possible problems to get you a little bit familiar with the use of this line of thinking and to use these methods.
come on ! are you really not understanding this ?
I think you are not trying to learn and get better, you try to get others doing your work for you.
these problems are so simple that stating them here costs you more time than just solving them.
remember fractions ?
remember the problems to find the smallest common denominator for a list of fractions ?
the first question is exactly that.
what is the smallest common denominator of 3/4, 1/3 and 1/2 ?
because that is the number you need to multiply both sides to eliminate all fractions.
so, what is the smallest number that can be split by 4, 3 and 2 ?
is it 2 ? no, 4 and 3 can't do that.
is it 3 ? no, 2 and 4 can't do that.
...
is it 6 ? no, 4 can't do that.
...
is it 8 ? no, 3 can't do that.
...
is it 12 ? yeah ! all 3 can do that.
here a little tip : you start by multiplying all involved numbers, and then work your way back by eliminating some factors shared by some of the numbers.
here it would be
2×3×4 = 24
but 12 is sufficient, because 2 and 4 share another common factor of 2. so, we can divide 24 by 2 and get 12.
"isolate the variable" means having it only on one side of the equation.
so, what do you think ?
subtracting any constants does not change anything for "j".
from all the offered options only the subtraction of 1.1j eliminates j from one side.
the runners save.
you only need to translate the words into the corresponding mathematical symbols.
runner 1 has $112 already saved.
that is our starting value for this runner.
so, 112 + ...
received a $45 gift card. so, $45 are added.
so, 112 + 45 + ...
saves $25 each month (m). so, whatever the number of m is, there will be $25×m added to the account.
so, 112 + 45 + 25m
we know already, it is the second option.
but for training purposes let's look at runner 2 too :
he starts with $50 already saved.
so, 50 + ...
saves $60 each month (m). same principle as above.
so, 50 + 60m
if we want to know, when (after how many months) both runners will have the same amount of money, we simply need to say both equations are equal and solve for m.
-3x + 1 + 10x = x + 4
how do we solve this ?
by bringing all x to one side and contract them into one expression. and try to bring all constants to the other side and contact them too. and then do the reverse operation of the x expression (like a division for a multiplication).
1 + 7x = x + 4
1 + 6x = 4
6x = 3
x = 3/6 = 1/2
hurray, it is the first option !