Word problem involving money
- Thread starter ashley
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i) Since the number of quarters is compared to the numbers of pennies and dimes, pick a variable for the number of quarters.
ii) If there are five fewer quarters than dimes, then there are five more dimes than quarters. Use this fact to create an expression, in terms of the variable you picked in (i), for the number of dimes.
iii) Using the same reasoning as in (ii), create an expression, in terms of the variable in (i), for the number of pennies.
iv) The value of each quarter is twenty-five cents. Then the value of two quarters is 2(25); the value of three is 3(25). Use this reasoning to create an expression, in terms of the variable in (i), for the value of the number of quarters.
v) Using the same reasoning as in (iv), create expressions for the values of the numbers of dimes and pennies.
vi) Using the expressions in (iv) and (v), create a sum for the total value of coins.
vii) Set the expression in (vi) equal to the given total value, written in cents.
viii) Solve the equation in (vii) for the value of the variable, which is the number of quarters.
ix) Back-solve for the numbers of dimes and pennies, using the relationships in (ii) and (iii).
If you get stuck, please reply showing how far you got. Thank you!
Eliz.
ii) If there are five fewer quarters than dimes, then there are five more dimes than quarters. Use this fact to create an expression, in terms of the variable you picked in (i), for the number of dimes.
iii) Using the same reasoning as in (ii), create an expression, in terms of the variable in (i), for the number of pennies.
iv) The value of each quarter is twenty-five cents. Then the value of two quarters is 2(25); the value of three is 3(25). Use this reasoning to create an expression, in terms of the variable in (i), for the value of the number of quarters.
v) Using the same reasoning as in (iv), create expressions for the values of the numbers of dimes and pennies.
vi) Using the expressions in (iv) and (v), create a sum for the total value of coins.
vii) Set the expression in (vi) equal to the given total value, written in cents.
viii) Solve the equation in (vii) for the value of the variable, which is the number of quarters.
ix) Back-solve for the numbers of dimes and pennies, using the relationships in (ii) and (iii).
If you get stuck, please reply showing how far you got. Thank you!
Eliz.
Selma paid a bill of $2.70 with quarters, dimes and pennies. She had 5 fewer quarters than dimes and 4 fewer quarters than pennies. How many coins of each kind did she use to pay the bill?
Let q, d and p equal the respective quantities of each coin.
If she had 5 fewer quarters than dimes, then q = d - 5 or d = q + 5.
If she had 4 fewer quarters than pennies, then q = p - 4 or p = q + 4.
If all the coins totaled $2.70, then .25q + .10d + .01p = 2.70 then 25q + 10d + 1p = 270.
Substitute (q + 5) and (q + 4) for d and p in 25p + 10d + p = 270 and you will have one equation with one unknown, q. Solve this equation for q and you are home free.
Let q, d and p equal the respective quantities of each coin.
If she had 5 fewer quarters than dimes, then q = d - 5 or d = q + 5.
If she had 4 fewer quarters than pennies, then q = p - 4 or p = q + 4.
If all the coins totaled $2.70, then .25q + .10d + .01p = 2.70 then 25q + 10d + 1p = 270.
Substitute (q + 5) and (q + 4) for d and p in 25p + 10d + p = 270 and you will have one equation with one unknown, q. Solve this equation for q and you are home free.