GED Math - Decimals and Fractions

Evaluate:

Do not use a calculator.

Explanation

Add vertically, aligning the decimal points:

$\begin{matrix} ; ;109.10 \ +; \underline{55.67} \ ; ; 164.77 \end{matrix}$

Above is the menu for a coffee shop; there is no sales tax charged on purchases.

Hedwig wants to throw an informal party for herself and seventeen guests. She wants to serve a large espresso and a butter croissant to each attendee, including herself. As luck would have it, the shop is having a special - for every two croissants purchased, the third is free. How much change will Hedwig get back for a $100 bill?

Explanation

There will be eighteen people at the party, including Hedwig.

She will spend $$3.29 \times 18 = $59.22$ for the large espressos.

"Buy two get one free" means that only two-thirds of the eighteen croissants - twelve of them - will be bought at the regular price, and the remaining six will be free. She will therefore spend $$2.29 \times 12 = $27.48$ .

The total purchase price will be .

The change from a $100 bill will be

One-fifth of what number is 19 ?

Explanation

To find a fraction of a whole number, we will multiply the fraction by the whole number. In this case, we do not know the whole number, but we do know the answer. So, we can substitute what we know. So, we get

$\frac{1}{5} \cdot x = 19$

Now, we will solve for x. We get

$\frac{1}{5} \cdot 5 \cdot x = 19 \cdot 5$

Evaluate $y ^{2} - 6y + 7$ for $y = 1 \frac{1}{2}$ .

Do not use a calculator.

$\frac{ 1}{4}$

$-13 \frac{3}{4}$

Explanation

$y = 1 \frac{1}{2} = \frac{3}{2}$ , so substitute $\frac{3}{2}$ for and follow the order of operations:

$y ^{2} - 6y + 7$

$= \left ( \frac{3}{2} \right )^{2} - 6 \left ( \frac{3}{2} \right ) + 7$

$= \left ( \frac{3^{2}}{2^{2}} \right ) - 6 \left ( \frac{3}{2} \right ) + 7$

$= \frac{9}{4} - 6 \left ( \frac{3}{2} \right ) + 7$

$=2 \frac{1}{4} - 6 \left ( \frac{3}{2} \right ) + 7$

$= 2 \frac{1}{4} - \left ( \frac{6 \times 3}{2} \right ) + 7$

$=2 \frac{1}{4} - \left ( \frac{18}{2} \right ) + 7$

$= 2 \frac{1}{4} -9+ 7$

$= -6\frac{3}{4} + 7$

$= \frac{ 1}{4}$

Above is the menu at a coffee shop.

Quincy has a coupon which he can use to get either a free butter croissant with the purchase of a large drink or one dollar off a butter croissant with the purchase of a small drink. The coupon says "limit one per coupon".

Quincy orders one large espresso, one small cafe latte, and two butter croissants. Disregarding tax, how much will he spend?

Explanation

Quincy will get one of the butter croissants for free, since he is also purchasing a large drink. He will pay for one large espresso, one small cafe latte, and one butter croissant. The total of their prices is:

$\begin{matrix} $3.29\ ; ; 3.09 \ +\underline{2.29} \ $8.67 \end{matrix}$

Above is the menu at a coffee shop.

Jimi, Noel, and Mitch each have a coupon that entitles the bearer to either one free butter croissant with the purchase of a large drink or one dollar off the price of a butter croissant with the purchase of a small drink. Each coupon says "limit one".

Jimi purchases one large cafe latte and one butter croissant; Noel purchases one small iced coffee and one butter croissant; Mitch purchases two butter croissants. Order the three from least amount spent to most.

Noel, Jimi, Mitch

Jimi, Noel, Mitch

Jimi, Mitch, Noel

Noel, Mitch, Jimi

Explanation

Jimi purchases a large drink, so he gets his butter croissant free. Therefore, he pays only for the large cafe latte. He spends $3.99.

Noel purchases a small drink, so he gets a $1 discount on his butter croissant. He spends $2.49 for the small iced coffee and $1.29 for the butter croissant - a total of .

Mitch does not buy any coffee so he will not use his coupon; he will pay for the two croissants. he will spend $$2.29 \times 2 = $4.58$ .

The three men, in ascending order by amount spent, are Noel, Jimi, and Mitch.

Above is the menu at a coffee shop. The shop is on a military base and does not charge sales tax.

Zola purchases three butter croissants and three cans of cola. She hands the cashier a $20 bill and gets $10.73 back in change. How much does one can of cola cost?

Explanation

Zola gets $10.73 in change for a $20 bill, so the price of her food and beverages is

She bought three butter croissants, which cost her

$$2.29 \times 3 = $6.87$ .

Subtract this from $9.27 to get the amount she spent on the cola.

She bought three cans for $2.40, so each can cost

$$2.40 \div 3 = $0.80$ .

Three inches on a map represents 100 miles of real distance. The distance between Adams and Monroe on a map is seven and a half inches. How many miles separate the two cities in reality?