Question

PLEASE HELP WILL FAN AND MEDAL!
Every evening Jenna empties her pockets and puts her change into a jar. At the end of the week she counts her money. One week she had 50 coins, all of them dimes and quarters. When she added them up, she had a total of $10.25. How many dimes did jenna have?

Answer 1

@phi

Answer 2

d= number of dimes and q= number of quarters.

Answer 3

you can solve this by finding two equations

ok with your "names"

now use this info:
she had 50 coins

can you make an equation using d, q and 50 ?

Answer 4

d+q=50?

Answer 5

yes, the number of dimes plus the number of quarters is 50

next, how much is a dime worth ? (in dollars)

Answer 6

10 cents

Answer 7

that's in cents. how about in dollars ?

Answer 8

0.10

Answer 9

next idea: how much is (for example) 4 dimes worth ?

Answer 10

0.40

Answer 11

and how did you figure that out ?

Answer 12

4*10

Answer 13

you either added up 0.10 four times: 0.10 + 0.10 + 0.10 + 0.10
or you multiplied 4 * 0.10
the 2nd way is faster

Answer 14

now if we have "d" dimes we still use the same idea: d dimes are worth d*0.10

Answer 15

how much are q quarters worth (in dollars, not cents) ?

Answer 16

0.25

Answer 17

so q*0.25?

Answer 18

yes 0.25 q

now we (sort of) know how much money we have:
0.10d + 0.25q

they tell us how much that adds up to. can you write an equation ?

Answer 19

0.10(d)+0.25(q)=$10.25

Answer 20

yes. now we have two equations and two unknowns
(if we have an equation for each unknown, we have enough info to solve the "system")

d+q=50
0.10(d)+0.25(q)=10.25 (I left off the dollar sign, but remember we are using dollars)

once we get to here, it's algebra and we use everything we know about solving system of equations (if we remember!)

Answer 21

if you multiply the bottom equation by 100, we can "get rid of" the decimals:
that means multiply both sides and all terms by 100

Answer 22

in other words, the 2nd equation can also be
10 d + 25 q = 1025

I notice each "coefficient" can be divided by 5, so I would do that
i.e. divide both sides and all terms by 5. we get

2 d + 5 q = 205

now we have


1 d + 1 q = 50
2 d + 5 q =205

Answer 23

ok so i just solved it and got d=15 q=35?

Answer 24

yes, that looks good. and they want the number of dimes

Answer 25

so its 15 thanks:D