Which expressions could complete this equation so that it has an infinite number of solutions?
9x -3(x +8)=
A. 6x - 24 <<<<<(I think this is one answer)
B. 6(x-3) +6C. 14 +5x -34D 8(x -3) - 2x
Christa buys 14 flowerpots. Some are small and cost $2.40 each. The rest are large and cost $5.60 each. She spends a total of $49.60. Which equation models this situation? Let s represent the number of small flowerpots she buys.
A. 5.6s + 2.4(s + 14) = 49.6
B. (2.4 + 9.6)(14 – s) = 49.6
C. 2.4s + 5.6(14 – s) = 49.6
D. 5.6s + 2.8(14) = 49.6
Mira has $760 in her bank account and withdraws $40 each month. Paulina has $210 in her bank account and deposits $70 each month. In how many months will Mira and Paulina have equal amounts of money in their accounts?
A. 5
B. 7
C. 8
D. 10
Answers
2.let number of small small pots she buys = s
total cost of small pots = 2.4s
Total number of pots bought = 14
So number of large pots bought = 14-s
total cost of large pots = 5.6(14-s)
Total cost = 2.4s + 5.6(14-s) = 49.6
3. Let they have same amount of money in x months.
Mira will have in her account = 760 - 40x
Paulina will have in her account = 210 + 70x
Since both have equal amount,
760 - 40x = 210 + 70x
⇒ -40x - 70x = 210 - 760
⇒-110x = -550
⇒ x = (-550)/ (-110)
⇒x = 5 months
Any value of x satisfies 6 x - 24 = 6 x - 24. Other options give only one value of x which the equation will be satisfied.
2. Option C. as the total cost is exactly = cost of small and big flowers together.
$ 49.6 = $ 2.4 s + $ 5.6 (14 – s)
evaluating it gives s = 9 and number of other flowers purchased are 5.
3. The difference in savings in bank = $ 760 - $ 210 = $ 550
The amount this difference is reducing every month = $ 70 + $ 40 = $ 100
So in $550/$110 = 5 months the amounts will be equal.