# Sample quiz on word problems using linear systems Main home here.

1. Let $x$ and $y$ be two numbers whose sum is $12$ and whose difference is $4$. If $x$ is the smaller number, the correct linear system is $\cdots$?
$x+y=12,~x-y=4$
$x-y=12,~x+y=4$
$x+y=12,~y-x=4$
$x-y=12,~x+y=-4$
2. $32$ is to be divided into two parts, $x$ and $y$. If $x=\frac{1}{4}y$, the correct linear system is $\cdots$?
$x+y=32,~x=\frac{1}{4}y$
$x-y=32,~x=\frac{1}{4}y$
$y=32x,~x=\frac{1}{4}y$
$x=32y,~x=\frac{1}{4}y$
3. Find two numbers whose sum is $13$ and whose difference is $5$.
$7$ and $6$
$9$ and $4$
$5$ and $8$
$10$ and $3$
4. Two numbers add up to $18$. Twice the first number added to the second number gives $27$. The numbers are $\cdots$
$8$ and $10$
$9$ and $9$
$11$ and $7$
$12$ and $6$
5. Divide $40$ into two parts, so that one part is two-thirds of the other.
$10,30$
$12,28$
$16,24$
$15,25$
6. Divide $100$ into two parts, so that one part is $\frac{9}{16}$ of the other
$36,64$
$18,82$
$30,70$
$28,72$
7. The digits of a two-digit number add up to $7$. If the digits are reversed, the number increases by $9$. Find the original number.
$43$
$25$
$34$
$52$
8. The digits of a two-digit number add up to $10$. If the digits are reversed, the number decreases by $36$. What is the original number?
$37$
$46$
$64$
$73$
9. A man has $\$5$notes and$\$10$ notes in his pocket. Altogether, he has $50$ notes that amount to $\$450$. How many of each denomination does he have?$20\times \$5$ and $30\times\$1010\times\$5$ and $40\times \$1040\times\$5$ and $10\times\$525\times\$5$ and $25\times\$10$10. Divide$72$into two parts, so that one part is$50\%$of the other.$28,5624,4832,6434,68\$