Mathematics Knowledge Practice Test 8

Correct answer: B — 3

Substitute the first equation $$(y = x + 4)$$ into the second equation: $$2x + (x + 4) = 13$$. Combine like terms: $$3x + 4 = 13$$. Subtract 4 from both sides: $$3x = 9$$. Finally, divide by 3: $$x = 3$$

Correct answer: A — $$60x^9$$

To multiply terms with coefficients and variables, multiply the coefficients together $$(5 \times 4 \times 3 = 60)$$ and add the exponents of the like base x according to the product rule $$(3 + 2 + 4 = 9)$$. This results in $$60x^9$$

Correct answer: C — 10

Let s be the smaller number and l be the larger number, so $$l = s + 6$$ (or $$s = l - 6$$). Substitute into the equation $$2s + 3l = 38$$: $$2(l - 6) + 3l = 38$$. Expand: $$2l - 12 + 3l = 38 \Rightarrow 5l - 12 = 38$$. Add 12: $$5l = 50 \Rightarrow l = 10$$

Correct answer: C — $48

Calculate the increase amount by finding 20% of the original price: $40 × 0.20 = $8. Add this increase to the original price: $40 + $8 = $48. Alternatively, multiply $40 by 1.20 to get $48 directly.

Correct answer: C — $$x = (\frac{3}{4})y$$

The rate of packing is 4 boxes per 3 minutes, meaning boxes per minute is $$\frac{4}{3}$$. Therefore, the number of boxes (y) equals $$(\frac{4}{3})$$ times the minutes (x), which is $$y = (\frac{4}{3})x$$. Rearranging to solve for x gives $$x = (\frac{3}{4})y$$, which matches Option C.

Correct answer: C — 14

Let Leo's current age be l, so his uncle's current age is $$3l$$. In 14 years, their ages will be $$(l + 14)$$ and $$(3l + 14)$$. According to the problem, $$l + 14 = 0.5(3l + 14)$$. Expanding gives $$l + 14 = 1.5l + 7$$. Subtract l from both sides: $$14 = 0.5l + 7$$. Subtract 7: $$7 = 0.5l$$, which means $$l = 14$$

Correct answer: C — 18

Let n be the number of nickels ($0.05) and d be the number of dimes ($0.10). We have $$n + d = 30$$, so $$d = 30 - n$$. The total value equation is $$0.05n + 0.10(30 - n) = 2.10$$. Expanding gives $$0.05n + 3.00 - 0.10n = 2.10 \Rightarrow -0.05n + 3.00 = 2.10$$. Subtract 3.00: $$-0.05n = -0.90$$. Divide by -0.05: $$n = 18$$ nickels.

Correct answer: C — 18

Let o be the number of $1 coins and q be the number of quarters ($0.25). We have $$o + q = 34$$, so $$q = 34 - o$$. The total value equation is $$1.00o + 0.25(34 - o) = 22.00$$. Expanding gives $$1.00o + 8.50 - 0.25o = 22.00 \Rightarrow 0.75o + 8.50 = 22.00$$. Subtract 8.50: $$0.75o = 13.50$$. Divide by 0.75: $$o = 18 1$$ coins.

Correct answer: B — $13

Let c be the amount spent at the commissary. According to the problem, $$4c - 5 = 47$$. Add 5 to both sides: $$4c = 52$$. Divide by 4: $$c = 13$$.

Correct answer: A — 12 and 72

Let the smaller number be x, so the larger number is $$6x$$. Their sum is $$x + 6x = 7x = 84$$. Solving for x gives $$x = 12$$. The larger number is $$6(12) = 72$$. Thus, the numbers are 12 and 72.