lynn has 8.58 in quarters and pennies. If she ha eight times as many pennies as quarters , how many of each does she have

Question

i need help

Answer 1

We can represent the information given with the following equations:

 

t = 8.58 (the total amount Lynn has is $8.58)

p = 8q (she has 8 x as many pennies as quarters)

 

We also know that pennies equal $0.01 and quarters equal $0.25, so:

 

t = 0.01p + 0.25q (the total amount Lynn has is equal to 0.01 x the number of pennies she has + 0.25 x the number of quarters she has)

 

Therefore:

 

8.58 = 0.01p + 0.25q

 

We can now substitute 8q for p to have only one variable in the equation, and then solve for q:

 

8.58 = 0.01(8q) + 0.25q

8.58 = 0.08q + 0.25q

8.58 = 0.33q

26 = q 

 

Lynn has 26 quarters. Now we need to find the number of pennies she has, and we have some options.

 

Option 1:

26 quarters = $6.50 (0.25(26) = 6.5)

 

$8.58 - $6.50 = $2.08 

$2.08/0.01 = 208 pennies 

 

Option 2:

 

p = 8q, and we solved q = 26

p = 8(26) = 208 pennies 

 

To check our answer, we plug these solved values into our earlier equation and check that it remains true:

 

8.58 = 0.01p + 0.25q

8.58 = 0.01(208) + 0.25(26)

8.58 = 2.08 + 6.50 

 

Given the above information, Lynn has 26 quarters and 208 pennies.