Inequality story problems
4. A purse contains 30 coins all either quarters or dimes. The total value of te coins is greater than $5.20. At least how many of the coins are quarters? How many are dimes?
8.A pair of consectuative integers has the property that 5 times the smaller is less than 4 times the greater. Find the greatest pair of intergers with this property.
11.A bank offers two types of checking accounts, Account A has a $4 maintenance fee each month and charges 10 cents for each check cashed. Account B has a $6 maintenance fee and charges 6 cents each check. What is the least number of checks that can be written each month for the "A" account to be more expensive?
Can you help me with those? If you could just give me the equation I can solve the rest most likely. Thank you so much!
4) 30coins = quarters + dimes
we are given that: quarters > $5.20
one quarter is .25, so 20 quarters is: 20(.25) = $5. however, 20 quarters < $5.20, so we must have an additional quarter to make that statement true giving us a total of 21 quarters. knowing this, we can now solve for dimes:
30 = 21 + dimes
30 - 21 = dimes
9 = dimes
8) let n be the small integer
let (n+1) be the consequitive larger integer
we are given:
5n < 4(n+1)
solving for n:
5n - 4n < 4
n < 4
A = $4(maintenance fee) + .10(check cashed)
B = $6(maintenance fee) + .06(check cashed)
so we wanna find out when is A > B:
$4 + .10x > $6 + .06x solve for x
4 - 6 > .06x - .10x
-2 > -(1/25)x
-2(-25) < x
50 < x
Thank you so much!!!