Card Jessica
How to solve each problem?
Jessica and Rebbecca collect baseball cards. Rebbecca has 5 times as many cards in her collection as Jessica has. Together they have a total of 216 cards. Use a system of simultaneous equations to determine how many cards each has.
Micah has 15 coins in his pocket, made up of dimes and quarters. The value of his coins is $2.25. Using a system of simultaneous equations, fine the number of dimes and the number of quarters in Micah's pocket.
j = Number of Jessica's cards
r = Number of Rebbecca's cards
5j=r
j + r = 216
j + 5j = 216
6j = 216
j = 36
r = 180
Rebbecca has 5 times more cards, so you have to multiply Jessica's cards by 5 to Make Them equal.
Jessica's cards plus Rebbecca's cards equals the total number of cards (216).
Substitute Rebbecca's cards for 5 times Jessica's cards (defined by the first equation).
Combine the cards.
Divide by 6.
Subtract Jessica's cards from the total, and you find that Rebbecca has 180 cards.
--------------------
d = Number of dimes
q = Number of quarters
10d + 25q = 225
d + q = 15
d + q = 15
q = 15 - d
10d + 25(15 - d) = 225
10d + 375 - 25d = 225
-15d + 375 = 225
15d - 375 = -225
15d = 150
d = 10
q = 5
This problem will be done using pennies, rather than dollars.
Multiply the number of dimes by their value (10). Do the same for the quarters.
The number of dimes plus the number of quarters equals the total number coins.
Second equation
Subtract d from both sides.
Substitute 15 - d for q.
Use the distributive property.
Combine the d's.
Multiply by -1.
Add 375 to both sides.
Divide by 15.
Subtract the number of dimes from the total, and you get the number of quarters, 5.
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