Kevin has 23 dimes and quarters in his piggy bank. If the value of these coins is $4.55, how many dimes and quarters does he have? Set up and solve a system of equations to solve the problem.

Question

briana.img · Answer

Been doing this problem for a while but I always get stuck at the distributive property

anonymous · Answer

that is a tough property that one
how far did you get?

briana.img · Answer

x+y=42 
7x+3y=194
7(42-y)+3y=194

anonymous · Answer

where in the world did $7x+3y=194$ come from ?

briana.img · Answer

oh wait this is my work for another problem sorry

anonymous · Answer

$$x+y=23\
25x+10y=455$$

briana.img · Answer

substitution method?

anonymous · Answer

sure i would have gone right to 
$$25x+10(23-x)=455$$ and skipped the first silliness
why use two variables when one will do

briana.img · Answer

25(23-y)+10y=455

briana.img · Answer

oh you're doing x first

anonymous · Answer

whatever
i solve for $x$ you solve for $y$
potato potahto

briana.img · Answer

25(23-y)+10y=455 
575-23y=455 

i always get messed up at this part

anonymous · Answer

whoa nellie hold the phone 
we are doing yours right ?$$25(23-y)+10y=455 $$

anonymous · Answer

leave the $10y$ term alone for a moment and multiply 
$$25(23-y)$$

briana.img · Answer

575y ?!

anonymous · Answer

yeah i see that
also you have $-23y$ which is also wrong

briana.img · Answer

yeah i haven't understood that fully

anonymous · Answer

$$25(23-y)=25\times 23-25\times y$$

anonymous · Answer

$$a(b-c)=ab-ac$$ that is the distributive law

briana.img · Answer

oh ok

anonymous · Answer

$$\huge \heartsuit (\clubsuit+\diamondsuit)=\heartsuit\times \clubsuit+\heartsuit\times \diamondsuit$$

anonymous · Answer

so the first step should be 
$$25(23-y)+10y=455\
25\times 23-23y+10y=455$$ then compute and combine like terms

briana.img · Answer

575-33y=455

anonymous · Answer

let me know when you get $$575 - 13 y == 455$$

radar · Answer

typo   change -23y to read -25y

anonymous · Answer

oh a see another problem here

anonymous · Answer

yeah i made a typo
should be 

$$25(23-y)+10y=455\
25\times 23-25y+10y=455$$

anonymous · Answer

then 
$$575 - 15 y = 455$$

briana.img · Answer

then subtract 575 from 455?!

anonymous · Answer

note that $-25y+10y=-15y$ it is the same as $10y-25y$

anonymous · Answer

yes

briana.img · Answer

15y=120
y=8

briana.img · Answer

x+8=23 
x=15

anonymous · Answer

k

anonymous · Answer

i mean yes you are right