James is two years younger than twice his sister kate’s age. together their ages add up to 19.
what is each of their ages?
identify(2pts): what is the problem? what do you
need to find or do? what will your final answer
look like? do you understand what is being
asked and what you need to do?
think(2pts): what have they told you? what does
it mean? what more do you know or can you
figure out? what connections can you make? do
you have a list of things you know, ideas to try &
a plan for doing it?
do(4pts): create and/or solve an equation (if
needed) & show steps towards completing the
problem. create an outline or map to organize
your answer. revise your plan if it doesn’t work
the first time.
answer(2 pts): look back at your work and
answer – does it make sense, answer all of the
questions, and is reasonable (accurate)? when it
is - organize and report your work and final answer.

answer:

153.2 gallons per day

step-by-step explanation:

to find out how much water he used each day, take the amount of water he used and divide by the number of days

1072.4 gallons / 7 days

153.2 gallons per day

answer:

all linear pairs are always supplementary

step-by-step explanation:

any two angles whose sum comes out to be 180° are said to be supplementary angles. these angles can be adjacent or not adjacent.

linear pair on the other hand is a pair of angles that are adjacent and their comes out to be 180° are linear pair. linear pair always form a line.

for example,

let us take two angles a= 110° and b=70°

the angles have been drawn in figure 1. notice that sum of two angles is 180° but these two angles are not adjacent and do not form a line. hence, these angles are only supplementary.

let us assume another angles a=120° and b=60°.

the angles have been drawn in figure 2. notice that sum of two angles is 180° and these two angles are also adjacent and do form a line. hence, these angles are not only supplementary but also linear.

hence, we can form a relationship between linear and supplementary that all linear pairs are always supplementary. but the inverse is not true.

answer:

12

step-by-step explanation:

let a = adele's current age

let t = timothy's current age

adele is 5 years older than timothy:

a = t + 5       {equation 1}

in 3 years timothy will be 2/3 of adele's age:

(2/3)(a + 3) = t + 3     {equation 2}

since we are looking for adele's age, let's rearrange equation 1 to:

t = a - 5

substitute that into equation 2 and solve for a.

(2/3)(a+3) = a - 5 + 3

(2/3)(a + 3) = a - 2

multiply through by 3 to clear the fraction

2(a+3) = 3a - 6

2a + 6 = 3a - 6

add 6 to both sides, subtract 2a from both sides

12 = a

adele is 12 years old

this means timothy is 7 years old.

check equation 2 to verify:

(2/3)(a + 3) = t + 3

(2/3)(12+3) = 7 + 3

(2/3)(15) = 10

10 = 10

answer is correct